problem solving with linear equations worksheet

Find here an unlimited supply of printable worksheets for solving linear equations, available as both PDF and html files. You can customize the worksheets to include one-step, two-step, or multi-step equations, variable on both sides, parenthesis, and more. The worksheets suit and courses (grades 6-9).

You can choose from SEVEN basic types of equations, ranging from simple to complex, explained below (such as one-step equations, variable on both sides, or having to use the distributive property). Customize the worksheets using the below.

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Key to Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language, and examples are easy to follow. Word problems relate algebra to familiar situations, helping students to understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system.

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Linear Equations Worksheets

Linear equations require students to work with a single variable of degree 1. So solving them are pretty simple and can be attempted by kids in grades 6-8.

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Linear Equations Worksheets

Here is a graphic preview for all of the Linear Equations Worksheets. You can select different variables to customize these Linear Equations Worksheets for your needs. The Linear Equations Worksheets are randomly created and will never repeat so you have an endless supply of quality Linear Equations Worksheets to use in the classroom or at home. Our Linear Equations Worksheets are free to download, easy to use, and very flexible.

These Linear Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Click here for a Detailed Description of all the Linear Equations Worksheets .

Quick Link for All Linear Equations Worksheets

Click the image to be taken to that linear equations worksheet., find the slope, of a graphed line.

Finding the Slope

Of a pair of points.

Find Properties

From a linear equation.

Graphing Lines

In slope-intercept form.

Graph Lines from

Y-intercept & point.

Graph Lines

In standard form.

Linear Equations

Linear Inequalities

Graphing Absolute

Value functions.

Detailed Description for All Linear Equations Worksheets

Finding Slope from a Graphed Line Worksheets These Linear Equations Worksheets will produce problems for practicing finding the slope from a graphed line. These Linear Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Finding Slope from a Pair of Points Worksheets These Linear Equations Worksheets will produce problems for practicing finding the slope from a pair of points. These Linear Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Finding Slope and the Y-intercept from a Linear Equation Worksheets These Linear Equations Worksheets will produce problems for practicing finding the slope and Y-intercept from an equation. You may select the type of problems to produce and the solutions that the students must perform. These Linear Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Graphing Lines in Slope-Intercept Form Worksheets These Linear Equations Worksheets will produce problems for practicing graphing lines in slope-intercept form. You may select the type of solutions that the students must perform. These Linear Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Graphing Lines Given Y-intercept and a Ordered Pair Worksheets These Linear Equations Worksheets will produce problems for practicing graphing lines given the Y-intercept and a ordered pair. You may select the type of solutions that the students must perform. These Linear Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Graphing Lines Given Two Ordered Pairs Worksheets These Linear Equations Worksheets will produce problems for practicing graphing lines given two ordered pairs. You may select the type of solutions that the students must perform. These Linear Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Graphing Lines in Standard Form Worksheets These Linear Equations Worksheets will produce problems for practicing graphing lines in standard form. You may select the type of solutions that the students must perform. These Linear Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Working with Linear Equations Worksheets These Linear Equations Worksheets will produce problems for practicing solving the equation of a linear equation. These Linear Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Writing Linear Equations Worksheets These Linear Equations Worksheets will produce problems for practicing writing linear equations from graphed lines. These Linear Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Graphing Linear Inequalities Worksheets These Inequality Worksheets will produce problems for practicing graphing linear inequalities. These Inequality Worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Graphing Absolute Values Worksheets These Linear Equations Worksheets will produce problems for practicing graphing absolute values. These Linear Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade.

Linear Equation Worksheets

These worksheets help reinforce students’ understanding of solving and graphing linear equations. The worksheets contain a variety of problems and exercises involving linear equations, ranging from basic to more complex scenarios. Students are tasked with solving equations for a single variable, identifying slope and intercepts, graphing linear equations on coordinate planes, and interpreting the meaning of solutions in real-world contexts. Linear Equation Worksheets provide valuable practice opportunities for students to hone their algebraic skills, build confidence in solving linear equations, and develop proficiency in graphing and interpreting linear relationships.

A Variable on Both Sides | Graphing Linear Equations

Slope | Growing Patterns | Speed, Time, and Distance

Two-Step Linear Equations | Linear Equation Word Problems

What Are Linear Equations?

Linear equations are fundamental mathematical expressions that describe the relationship between two variables in a straight line. They are among the simplest and most important equations in algebra and are widely used in various fields such as physics, engineering, economics, and social sciences. A linear equation can be expressed in the form:

y is the dependent variable, representing the output or value being measured.

x is the independent variable, representing the input or variable that is manipulated.

m is the slope of the line, indicating the rate of change or steepness of the line.

b is the y-intercept, representing the point where the line crosses the y-axis when x = 0

Linear equations can also be written in different forms to emphasize different aspects of the equation. One common form is the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. This form is particularly useful for graphing linear equations since it directly provides the slope and y-intercept of the line.

Another form is the standard form A x + B y = C, where A, B, and C are constants. In this form, the coefficients A and B determine the slope of the line, while C determines the y-intercept when the equation is rearranged into slope-intercept form.

Linear equations can also be expressed in point-slope form y – y 1 = m(x – x 1 ), where m is the slope of the line, and (x 1 , y 1 )is a point on the line. This form is useful for finding the equation of a line given its slope and a point it passes through.

The graph of a linear equation is a straight line on a Cartesian coordinate plane. The slope of the line determines its steepness: a positive slope indicates a line that rises as x increases, while a negative slope indicates a line that falls as x increases. A slope of zero results in a horizontal line, while an undefined slope corresponds to a vertical line.

Linear equations are used to model various real-world phenomena, such as the relationship between distance and time in motion problems, the relationship between supply and demand in economics, or the trajectory of a projectile in physics. They provide a powerful tool for analyzing and predicting behavior in situations where there is a linear relationship between two variables. Overall, linear equations serve as a foundational concept in algebra and play a crucial role in numerous applications across different fields of study.

What Are The Parts of a Linear Equation?

A linear equation is a mathematical expression that represents the relationship between two variables in a straight line. Let’s break down the different parts of a linear equation:

• Variables: In a linear equation, typically denoted as y = mx + b, there are two variables:

x: The independent variable represents the input or the variable that can be manipulated or controlled.

y: The dependent variable represents the output or the variable whose value depends on the value of the independent variable.

• Slope (m): The slope of a line is a measure of its steepness or incline. It indicates how much the dependent variable (y) changes for a given change in the independent variable (x).

A positive slope (m > 0) indicates that as the value of x increases, the value of y also increases, resulting in an upward sloping line.

A negative slope (m < 0) indicates that as the value of x increases, the value of y decreases, resulting in a downward sloping line.

A slope of zero (m = 0) results in a horizontal line where y remains constant regardless of changes in x.

An undefined slope occurs when the line is vertical, meaning that x remains constant while y can vary.

• Y-intercept (b): The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is equal to zero.

It is denoted as the ordered pair (0, b), where b is the y-coordinate of the point of intersection with the y-axis.

The y-intercept determines the initial value or the starting point of the line on the y-axis.

Equation Forms: Linear equations can be represented in various forms, each highlighting different aspects of the equation.

Slope-intercept form (y = mx + b): This form directly reveals the slope (m) and y-intercept (b) of the line.

Standard form (A x + B y = C): In this form, A, B, and C are constants, and it’s useful for easily identifying the x-intercept and y-intercept of the line.

Point-slope form (y – y 1 = m (x -x 1 )) : This form allows the equation to be written given a point (x 1 , y 1 )on the line and its slope (m).

Understanding the different parts of a linear equation allows us to interpret and manipulate equations to represent relationships between variables graphically and algebraically. It also enables us to solve problems, analyze data, and make predictions in various real-world contexts where linear relationships exist.

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ChangeMe: Worksheets with Answers

Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers.

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Mathster is a fantastic resource for creating online and paper-based assessments and homeworks. They have kindly allowed me to create 3 editable versions of each worksheet, complete with answers.

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Solve Linear Equations Word Problems Worksheets

Related Topics: More Math Worksheets More Printable Math Worksheets More Grade 7 Math Lessons Grade 8 Math Worksheets

Printable “Algebra” worksheets: Write Equations Using Symbols Write Linear & Nonlinear Expressions Write & Solve Linear Equations Solve Linear Equations (Distributive) Solve Linear Equations in Disguise Solve Linear Equations Word Problems

Examples, solutions, videos, and worksheets to help Grade 7 and Grade 8 learn how to write and solve linear equation word problems.

How to solve linear equation word problems?

Solving linear equation word problems involves translating the problem from words into a mathematical equation and then solving that equation. Here’s a step-by-step guide:

• Read the Problem Carefully
• Understand what the problem is asking.
• Identify the key information provided in the problem.
• Define the Variables
• Assign variables to the unknown quantities you’re trying to find.
• Set Up the Equation
• Translate the words into a mathematical equation using the variable(s) you defined.
• Identify relationships such as “sum,” “difference,” “product,” and “quotient” to form the equation.
• Solve the Equation
• Use algebraic methods to solve the equation for the unknown variable(s).
• This might involve adding, subtracting, multiplying, dividing, or using the distributive property.
• Check Your Solution
• Substitute your solution back into the original problem to ensure it satisfies all conditions.
• Answer the Question
• Provide the final answer in the context of the problem.

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Solve linear equations word problems Worksheets .

More Solve linear equations word problems Worksheets

Printable (Answers on the second page.) Solve linear equations word problems Worksheet #1 Solve linear equations word problems Worksheet #2 Solve linear equations word problems Worksheet #3 Solve linear equations word problems Worksheet #4 Solve linear equations word problems Worksheet #5

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Linear Equation Worksheets. Free worksheets with answer keys

Enjoy these free printable worksheets . Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

• Mixed Problems on Writing Equations of Lines
• Slope Intercept Form Worksheet
• Standard Form Worksheet
• Point Slope Worksheet
• Write Equation of Line From the Slope and 1 Point
• Write Equation of Line From Two Points
• Equation of Line Parallel to Another Line and Through a Point
• Equation of Line Perpendicular to Another Line and Through a Point
• Slope of a Line
• Perpendicular Bisector of Segment
• Write Equation of Line Mixed Review
• Word Problems

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Word Problems Linear Equations

Andymath.com features free videos, notes, and practice problems with answers! Printable pages make math easy. Are you ready to be a mathmagician?

\(\textbf{1)}\) Joe and Steve are saving money. Joe starts with $105 and saves $5 per week. Steve starts with $5 and saves $15 per week. After how many weeks do they have the same amount of money? Show Equations \(y= 5x+105,\,\,\,y=15x+5\) Show Answer 10 weeks ($155)

\(\textbf{2)}\) mike and sarah collect rocks. together they collected 50 rocks. mike collected 10 more rocks than sarah. how many rocks did each of them collect show equations \(m+s=50,\,\,\,m=s+10\) show answer mike collected 30 rocks, sarah collected 20 rocks., \(\textbf{3)}\) in a classroom the ratio of boys to girls is 2:3. there are 25 students in the class. how many are girls show equations \(b+g=50,\,\,\,3b=2g\) show answer 15 girls (10 boys), \(\textbf{4)}\) kyle makes sandals at home. the sandal making tools cost $100 and he spends $10 on materials for each sandal. he sells each sandal for $30. how many sandals does he have to sell to break even show equations \(c=10x+100,\,\,\,r=30x\) show answer 5 sandals ($150), \(\textbf{5)}\) molly is throwing a beach party. she still needs to buy beach towels and beach balls. towels are $3 each and beachballs are $4 each. she bought 10 items in total and it cost $34. how many beach balls did she get show equations show answer 4 beachballs (6 towels), \(\textbf{6)}\) anna volunteers at a pet shelter. they have cats and dogs. there are 36 pets in total at the shelter, and the ratio of dogs to cats is 4:5. how many cats are at the shelter show equations \(c+d=40,\,\,\,5d=4c\) show answer 20 cats (16 dogs), \(\textbf{7)}\) a store sells oranges and apples. oranges cost $1.00 each and apples cost $2.00 each. in the first sale of the day, 15 fruits were sold in total, and the price was $25. how many of each type of frust was sold show equations \(o+a=15,\,\,\,1o+2a=25\) show answer 10 apples and 5 oranges, \(\textbf{8)}\) the ratio of red marbles to green marbles is 2:7. there are 36 marbles in total. how many are red show equations \(r+g=36,\,\,\,7r=2g\) show answer 8 red marbles (28 green marbles), \(\textbf{9)}\) a tennis club charges $100 to join the club and $10 for every hour using the courts. write an equation to express the cost \(c\) in terms of \(h\) hours playing tennis. show equation the equation is \(c=10h+100\), \(\textbf{10)}\) emma and liam are saving money. emma starts with $80 and saves $10 per week. liam starts with $120 and saves $6 per week. after how many weeks will they have the same amount of money show equations \(e = 10x + 80,\,\,\,l = 6x + 120\) show answer 10 weeks ($180 each), \(\textbf{11)}\) mark and lisa collect stamps. together they collected 200 stamps. mark collected 40 more stamps than lisa. how many stamps did each of them collect show equations \(m + l = 200,\,\,\,m = l + 40\) show answer mark collected 120 stamps, lisa collected 80 stamps., \(\textbf{12)}\) in a classroom, the ratio of boys to girls is 3:5. there are 40 students in the class. how many are boys show equations \(b + g = 40,\,\,\,5b = 3g\) show answer 15 boys (25 girls), \(\textbf{13)}\) lisa is selling handmade jewelry. the materials cost $60, and she sells each piece for $20. how many pieces does she have to sell to break even show equations \(c=60,\,\,\,r=20x\) show answer 3 pieces, \(\textbf{14)}\) tom is buying books and notebooks for school. books cost $15 each, and notebooks cost $3 each. he bought 12 items in total, and it cost $120. how many notebooks did he buy show equations \(b + n = 12,\,\,\,15b+3n=120\) show answer 5 notebooks (7 books), \(\textbf{15)}\) emily volunteers at an animal shelter. they have rabbits and guinea pigs. there are 36 animals in total at the shelter, and the ratio of guinea pigs to rabbits is 4:5. how many guinea pigs are at the shelter show equations \(r + g = 36,\,\,\,5g=4r\) show answer 16 guinea pigs (20 rabbits), \(\textbf{16)}\) mike and sarah are going to a theme park. mike’s ticket costs $40, and sarah’s ticket costs $30. they also bought $20 worth of food. how much did they spend in total show equations \(m + s + f = t,\,\,\,m=40,\,\,\,s=30,\,\,\,f=20\) show answer they spent $90 in total., \(\textbf{17)}\) the ratio of red marbles to blue marbles is 2:3. there are 50 marbles in total. how many are blue show equations \(r + b = 50,\,\,\,3r=2b\) show answer 30 blue marbles (20 red marbles), \(\textbf{18)}\) a pizza restaurant charges $12 for a large pizza and $8 for a small pizza. if a customer buys 5 pizzas in total, and it costs $52, how many large pizzas did they buy show equations \(l + s = 5,\,\,\,12l+8s=52\) show answer they bought 3 large pizzas (2 small pizzas)., \(\textbf{19)}\) the area of a rectangle is 48 square meters. if the length is 8 meters, what is the width of the rectangle show equations \(a=l\times w,\,\,\,l=8,\,\,\,a=48\) show answer the width is 6 meters., \(\textbf{20)}\) two numbers have a sum of 50. one number is 10 more than the other. what are the two numbers show equations \(x+y=50,\,\,\,x=y+10\) show answer the numbers are 30 and 20., \(\textbf{21)}\) a store sells jeans for $40 each and t-shirts for $20 each. in the first sale of the day, they sold 8 items in total, and the price was $260. how many of each type of item was sold show equations \(j+t=8,\,\,\,40j+20t=260\) show answer 5 jeans and 3 t-shirts were sold., \(\textbf{22)}\) the ratio of apples to carrots is 3:4. there are 28 fruits in total. how many are apples show equations \(\)a+c=28,\,\,\,4a=3c show answer there are 12 apples and 16 carrots., \(\textbf{23)}\) a phone plan costs $30 per month, and there is an additional charge of $0.10 per minute for calls. write an equation to express the cost \(c\) in terms of \(m\) minutes. show equation the equation is \(\)c=30+0.10m, \(\textbf{24)}\) a triangle has a base of 8 inches and a height of 6 inches. calculate its area. show equations \(a=0.5\times b\times h,\,\,\,b=8,\,\,\,h=6\) show answer the area is 24 square inches., \(\textbf{25)}\) a store sells shirts for $25 each and pants for $45 each. in the first sale of the day, 4 items were sold, and the price was $180. how many of each type of item was sold show equations \(t+p=4,\,\,\,25t+45p=180\) show answer 0 shirts and 4 pants were sold., \(\textbf{26)}\) a garden has a length of 12 feet and a width of 10 feet. calculate its area. show equations \(a=l\times w,\,\,\,l=12,\,\,\,w=10\) show answer the area is 120 square feet., \(\textbf{27)}\) the sum of two consecutive odd numbers is 56. what are the two numbers show equations \(x+y=56,\,\,\,x=y+2\) show answer the numbers are 27 and 29., \(\textbf{28)}\) a toy store sells action figures for $15 each and toy cars for $5 each. in the first sale of the day, 10 items were sold, and the price was $110. how many of each type of item was sold show equations \(a+c=10,\,\,\,15a+5c=110\) show answer 6 action figures and 4 toy cars were sold., \(\textbf{29)}\) a bakery sells pie for $2 each and cookies for $1 each. in the first sale of the day, 14 items were sold, and the price was $25. how many of each type of item was sold show equations \(p+c=14,\,\,\,2p+c=25\) show answer 11 pies and 3 cookies were sold., \(\textbf{for 30-33}\) two car rental companies charge the following values for x miles. car rental a: \(y=3x+150 \,\,\) car rental b: \(y=4x+100\), \(\textbf{30)}\) which rental company has a higher initial fee show answer company a has a higher initial fee, \(\textbf{31)}\) which rental company has a higher mileage fee show answer company b has a higher mileage fee, \(\textbf{32)}\) for how many driven miles is the cost of the two companies the same show answer the companies cost the same if you drive 50 miles., \(\textbf{33)}\) what does the \(3\) mean in the equation for company a show answer for company a, the cost increases by $3 per mile driven., \(\textbf{34)}\) what does the \(100\) mean in the equation for company b show answer for company b, the initial cost (0 miles driven) is $100., \(\textbf{for 35-39}\) andy is going to go for a drive. the formula below tells how many gallons of gas he has in his car after m miles. \(g=12-\frac{m}{18}\), \(\textbf{35)}\) what does the \(12\) in the equation represent show answer andy has \(12\) gallons in his car when he starts his drive., \(\textbf{36)}\) what does the \(18\) in the equation represent show answer it takes \(18\) miles to use up \(1\) gallon of gas., \(\textbf{37)}\) how many miles until he runs out of gas show answer the answer is \(216\) miles, \(\textbf{38)}\) how many gallons of gas does he have after 90 miles show answer the answer is \(7\) gallons, \(\textbf{39)}\) when he has \(3\) gallons remaining, how far has he driven show answer the answer is \(162\) miles, \(\textbf{for 40-42}\) joe sells paintings. each month he makes no commission on the first $5,000 he sells but then makes a 10% commission on the rest., \(\textbf{40)}\) find the equation of how much money x joe needs to sell to earn y dollars per month. show answer the answer is \(y=.1(x-5,000)\), \(\textbf{41)}\) how much does joe need to sell to earn $10,000 in a month. show answer the answer is \($105,000\), \(\textbf{42)}\) how much does joe earn if he sells $45,000 in a month show answer the answer is \($4,000\), see related pages\(\), \(\bullet\text{ word problems- linear equations}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- averages}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- consecutive integers}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- distance, rate and time}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- break even}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- ratios}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- age}\) \(\,\,\,\,\,\,\,\,\), \(\bullet\text{ word problems- mixtures and concentration}\) \(\,\,\,\,\,\,\,\,\), linear equations are a type of equation that has a linear relationship between two variables, and they can often be used to solve word problems. in order to solve a word problem involving a linear equation, you will need to identify the variables in the problem and determine the relationship between them. this usually involves setting up an equation (or equations) using the given information and then solving for the unknown variables . linear equations are commonly used in real-life situations to model and analyze relationships between different quantities. for example, you might use a linear equation to model the relationship between the cost of a product and the number of units sold, or the relationship between the distance traveled and the time it takes to travel that distance. linear equations are typically covered in a high school algebra class. these types of problems can be challenging for students who are new to algebra, but they are an important foundation for more advanced math concepts. one common mistake that students make when solving word problems involving linear equations is failing to set up the problem correctly. it’s important to carefully read the problem and identify all of the relevant information, as well as any given equations or formulas that you might need to use. other related topics involving linear equations include graphing and solving systems. understanding linear equations is also useful for applications in fields such as economics, engineering, and physics., about andymath.com, andymath.com is a free math website with the mission of helping students, teachers and tutors find helpful notes, useful sample problems with answers including step by step solutions, and other related materials to supplement classroom learning. if you have any requests for additional content, please contact andy at [email protected] . he will promptly add the content. topics cover elementary math , middle school , algebra , geometry , algebra 2/pre-calculus/trig , calculus and probability/statistics . in the future, i hope to add physics and linear algebra content. visit me on youtube , tiktok , instagram and facebook . andymath content has a unique approach to presenting mathematics. the clear explanations, strong visuals mixed with dry humor regularly get millions of views. we are open to collaborations of all types, please contact andy at [email protected] for all enquiries. to offer financial support, visit my patreon page. let’s help students understand the math way of thinking thank you for visiting. how exciting.

8th Grade Linear Equations Worksheets

Linear equations are equations that have two variables and when graphed are a straight line based on their slope and y-intercept. Hence,8th grade linear equations worksheets have a variety of questions that help students practice key concepts and build a rock-solid foundation of the concepts.

Benefits of Linear Equations Grade 8 Worksheets

Linear equation worksheets are a great resource for students to practice a large variety of problems. These 8th grade math worksheets are supported by visuals which help students get a crystal clear understanding of the topic. The variety of problems that these worksheets offer helps students approach these concepts in an engaging and fun manner.

Many websites might provide similar worksheets but the Cuemath 8th grade linear equations worksheets come with visual simulation for students to see the problems in action, an answer key that provides a detailed step-by-step solution for students to understand the process better, and a worksheet with detailed solutions.

Printable PDFs for Grade 8 Linear Equations Worksheets

Students can practice problems by downloading the linear equations grade 8 worksheets in PDF format for free.

• Math 8th Grade Linear Equations Worksheet
• 8th Grade Linear Equations Math Worksheet
• Eighth Grade Linear Equations Worksheet
• Grade 8 Math Linear Equations Worksheet

Explore more topics at Cuemath's Math Worksheets .

Worksheet on Linear Equations

Practice worksheet on linear equations in one variable. Students can recall the lesson and practice the equations step-by-step and then try to represent the solution of the linear equation graphically.

1. Solve each of the following equations and represent the solution graphically.   (a) 7x + 2 = -19   (b) 3x - 1/3 = 5    (c) 5x - 4 = 21   (d) -7x = 21    (e) 18 - 7x = -3    (f) 3(x + 4) = 21    (g) 2x/3 - 3x/5 = 8    (h) 3x - 9 = 5x - 3    (i) 3(x - 3) = 4(2x + 1) 

2. Solve each of the following equations and check your solution by substituting in the equation. 

  (a) 3x/2 - 10 = 1/2   (b) x/2 - x/3 = 8   (c) 6x - 9 - 2(1 - x) = x + 9   (d) 2(x - 2) - 5(x - 5) = 4(x - 8) - 2(x - 2)   (e) (2 - y)/(y + 7) = 3/5   (f) (3x + 2)/(2x - 3) = - 3/2   (g) (x - 8 )/3 = (x - 3)/5   (h) 0.25(4y - 3) = 0.5y - 9

Answers for the worksheet on linear equations in one variable are given below so that students can check the exact answers after solving the equations.

1.  (a) -3   (b) 1⁷/₉   (c) 5   (d) -3   (e) 3   (f) 3   (g) 120   (h) -3   (i) -2³/₅

●   Equations

What is an Equation?

What is a Linear Equation?

How to Solve Linear Equations?

Solving Linear Equations

Problems on Linear Equations in One Variable

Word Problems on Linear Equations in One Variable

Practice Test on Linear Equations

Practice Test on Word Problems on Linear Equations

●   Equations - Worksheets

Worksheet on Word Problems on Linear Equation

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Absolute Value Equations Worksheets

Zero Solutions

Absolute Practice

Fraction Focus

Value Voyages

Absolute Essentials

Value Variations

Value Vortex

Absolute Adventures

Value Ventures

Absolute Challenges

Absolute Answers

Distance Decisions

Value Quest

Absolute Mastery

About these 15 worksheets.

These worksheets are a vital resource designed to help students grasp the concept of absolute value and how it interacts with algebraic equations. These worksheets typically present a range of problems that require students to solve equations where the variable is within an absolute value expression. The unique challenge of these equations lies in the fact that absolute value represents the distance of a number from zero on the number line, meaning it is always non-negative. Therefore, when solving absolute value equations, students must consider both the positive and negative scenarios that could satisfy the equation.

These worksheets come in various formats, each targeting different aspects of solving absolute value equations. Some worksheets start with more straightforward problems where the absolute value expression is set equal to a number. For instance, a problem might ask students to solve an equation like ∣x + 3∣ = 7. Here, students must recognize that the equation has two potential solutions – x + 3 = 7 and x + 3 = -7, leading to two different values for x. This type of problem introduces students to the fundamental idea that absolute value equations often have two solutions, a concept that is critical for understanding more complex algebraic topics.

As students progress, worksheets may include problems where the absolute value expression is equal to zero or involves more complicated expressions within the absolute value bars. For example, solving ∣2x – 5∣ = 0 teaches students that the only solution occurs when the expression inside the absolute value is zero, reinforcing the idea that absolute value represents distance, which can only be zero if the point is at the origin. This type of problem helps students develop a deeper understanding of how absolute value works and its implications for solving equations.

More advanced worksheets might present absolute value equations where students have to deal with variables on both sides of the equation or equations that involve additional operations outside of the absolute value. For example, solving an equation like ∣3x + 4∣ = 2x + 5 requires students to not only consider the two cases of the absolute value expression but also manage the algebraic manipulation needed to isolate the variable. These problems challenge students to apply their knowledge of both absolute value and algebraic operations, encouraging them to think critically about how to approach and solve more complex equations.

In addition to these basic types of problems, some worksheets introduce inequalities involving absolute values, such as solving ∣x – 3∣ > 5. These problems require students to understand that the inequality represents a range of values for x that satisfy the condition, which can result in two separate inequalities to solve. This type of exercise teaches students how absolute value can create intervals on the number line and how to interpret these intervals within the context of inequality solutions.

The series of practice worksheets also includes a variety of problem types that cater to different learning levels. Beginner worksheets focus on equations where the absolute value expression is set equal to a constant, helping students get comfortable with the basic concept. Intermediate worksheets introduce more complex expressions within the absolute value or include operations outside the absolute value, requiring additional algebraic steps. Advanced worksheets cover absolute value inequalities and equations with variables on both sides, providing challenges that push students to apply their knowledge in new and more demanding ways.

The collection also includes worksheets that address common misconceptions and errors in solving absolute value equations. For example, problems where the absolute value expression is set equal to a negative number, such as ∣x + 2∣ = -3, can be used to reinforce the idea that absolute value cannot be negative, leading to no solution. These types of problems help students understand the boundaries of what absolute value can represent and how it applies in different contexts.

We also have word problems involving absolute value. These problems can help students see the practical applications of absolute value equations in real-world scenarios, such as determining distances, differences, or deviations from a standard value. For example, a word problem might ask students to find the maximum and minimum possible values of a quantity that is allowed to vary by a certain amount, introducing them to the concept of tolerance in manufacturing or quality control.

The collection also includes worksheets that integrate absolute value equations with other algebraic concepts, such as systems of equations, quadratic equations, or even basic functions. For instance, a worksheet might ask students to solve a system of equations where one equation involves an absolute value expression. This type of problem encourages students to think about how different algebraic concepts interact and how absolute value can affect the solution set of an equation.

What Are Absolute Value Equations?

Absolute value equations are mathematical equations that involve the absolute value of a variable expression. The absolute value of a number is its distance from zero on the number line, regardless of direction, which means it is always non-negative. For example, the absolute value of both -5 and 5 is 5. When solving an absolute value equation, such as ∣x – 3∣ = 7, you must consider both the positive and negative solutions that satisfy the equation x – 3 = 7 and x – 3 = -7, leading to the solutions x = 10 and x = -4.

In the real world, the skill of solving absolute value equations is useful in various situations where distance, deviation, or tolerance is involved. For example:

Engineering and Manufacturing – Engineers often work with tolerances, which are acceptable ranges of variation in measurements. For instance, if a machine part is supposed to be exactly 10 mm but can be within 0.1 mm of that measurement, the acceptable measurements can be expressed as ∣x – 10∣ ≤ 0.1, where x represents the actual measurement. Solving this absolute value inequality helps determine the acceptable range of measurements.

Finance – In financial analysis, absolute value equations can be used to calculate deviations in stock prices, interest rates, or other financial metrics from a given benchmark. For example, an investor might want to know how far a stock price can deviate from its average value over a certain period.

Quality Control – In quality control processes, absolute value equations are used to determine how much a product’s characteristics (like weight, size, or concentration) deviate from the desired standard. This ensures products remain within acceptable quality limits.

Navigation and Distance Calculation – Absolute value is used in navigation to determine the distance between two points on a map, regardless of direction. For example, if you’re calculating the distance between two locations along a straight path, the absolute value can help determine how far you need to travel in either direction.

Understanding and solving absolute value equations allows individuals to handle these and other practical situations that require consideration of both positive and negative deviations from a specific value, ensuring accurate and reliable results in real-world applications.