A store is having a sale where every shirt costs $$x$$ dollars. If you buy 3 shirts and spend a total of $$45$$ , write an equation to represent this situation and solve for $$x$$ . Justify each step using the properties of equality.

$$3x = 45$$ , so $$x = 15$$ by dividing both sides by 3 (Division Property of Equality)

$$x + 3 = 45$$ , so $$x = 42$$ by subtracting 3 from both sides

$$3 + x = 45$$ , so $$x = 42$$ by subtracting 3 from both sides

$$x = 45 \times 3$$ , so $$x = 135$$

Solve the equation $$5x - 7 = 18$$ and justify each step using the properties of equality.

Add 7 to both sides: $$5x = 25$$ , then divide by 5: $$x = 5$$

Subtract 5 from both sides: $$x - 7 = 13$$ , then add 7: $$x = 20$$

Add 18 to both sides: $$5x + 11 = 0$$ , then divide by 5: $$x = -2.2$$

Multiply both sides by 7: $$35x - 49 = 126$$ , then add 49: $$35x = 175$$

A taxi company charges a flat fee of $$4$$ dollars plus $$2$$ dollars per mile. Write a linear equation to represent the total cost $$C$$ for $$m$$ miles, and find the cost for $$6$$ miles.

$$C = 2m + 4$$ , so $$C = 2(6) + 4 = 16$$

$$C = 4m + 2$$ , so $$C = 4(6) + 2 = 26$$

$$C = 6m + 2$$ , so $$C = 6(6) + 2 = 38$$

$$C = 2m - 4$$ , so $$C = 2(6) - 4 = 8$$

Solve the equation $$2(x + 3) = 16$$ and justify each step using the properties of equality.

Divide both sides by 2: $$x + 3 = 8$$ , then subtract 3: $$x = 5$$

Subtract 3 from both sides: $$2x = 13$$ , then divide by 2: $$x = 6.5$$

Add 3 to both sides: $$2x = 19$$ , then divide by 2: $$x = 9.5$$

Multiply both sides by 3: $$6(x + 3) = 48$$ , then subtract 3: $$6x = 45$$

A movie theater sells tickets for $$y$$ dollars each. If 8 tickets cost $$56$$ , write an equation to represent this situation and solve for $$y$$ .

$$y = 56 \times 8$$ , so $$y = 448$$

Solve the equation $$4x + 9 = 25$$ and justify each step using the properties of equality.

Subtract 9 from both sides: $$4x = 16$$ , then divide by 4: $$x = 4$$

Add 9 to both sides: $$4x = 34$$ , then divide by 4: $$x = 8.5$$

Divide both sides by 4: $$x + 2.25 = 6.25$$ , then subtract 2.25: $$x = 4$$

Multiply both sides by 9: $$36x + 81 = 225$$ , then subtract 81: $$36x = 144$$

A gym membership costs a one-time fee of $$25$$ dollars plus $$15$$ dollars per month. Write a linear equation for the total cost $$T$$ after $$m$$ months, and find the cost after $$4$$ months.

$$T = 15m + 25$$ , so $$T = 15(4) + 25 = 85$$

$$T = 25m + 15$$ , so $$T = 25(4) + 15 = 115$$

$$T = 4m + 25$$ , so $$T = 4(4) + 25 = 41$$

$$T = 15m - 25$$ , so $$T = 15(4) - 25 = 35$$

Solve the equation $$7x - 4 = 3x + 12$$ and justify each step using the properties of equality.

Subtract $$3x$$ from both sides: $$4x - 4 = 12$$ , add 4: $$4x = 16$$ , divide by 4: $$x = 4$$

Add $$4$$ to both sides: $$7x = 3x + 16$$ , subtract $$3x$$ : $$4x = 16$$ , divide by 4: $$x = 4$$

Subtract $$12$$ from both sides: $$7x - 16 = 3x$$ , subtract $$3x$$ : $$4x - 16 = 0$$ , add $$16$$ : $$4x = 16$$ , divide by 4: $$x = 4$$

A student has $$x$$ dollars. After spending $$12$$ , she has $$23$$ dollars left. Write an equation to represent this situation and solve for $$x$$ .

$$x - 12 = 23$$ , so $$x = 35$$

$$x + 12 = 23$$ , so $$x = 11$$

$$x = 23 \times 12$$ , so $$x = 276$$

$$x = 23 - 12$$ , so $$x = 11$$

Solve the equation $$3(x - 2) + 5 = 20$$ and justify each step using the properties of equality.

Subtract 5 from both sides: $$3(x - 2) = 15$$ , divide by 3: $$x - 2 = 5$$ , add 2: $$x = 7$$

Add 5 to both sides: $$3(x - 2) = 25$$ , divide by 3: $$x - 2 = 8.33$$ , add 2: $$x = 10.33$$

Divide both sides by 3: $$(x - 2) + \frac{5}{3} = \frac{20}{3}$$ , subtract $$\frac{5}{3}$$ : $$x - 2 = 5$$ , add 2: $$x = 7$$

Multiply both sides by 2: $$6(x - 2) + 10 = 40$$ , subtract 10: $$6(x - 2) = 30$$ , divide by 6: $$x - 2 = 5$$ , add 2: $$x = 7$$

The equation $$8\left(x+3\right)=\ -16$$ is solved in several steps below. For each step, choose the reason that best justifies it.

Subtraction Property of Equality

The property used between step 1 and step 2 is

Commutative Property of addition

Consider the steps in solving an equation shown below. What property justifies the work completed between Step #2 and Step #3?

Associative Property of Addition

Move a property into each box of the reason column to justify each step.

Multiplication Property of Equality

Subtraction Property of Equality

Justify the steps of Solving Linear Equations

Authored by Yusufu Musana

Mathematics

9th Grade

VA covered

Used 5+ times

Justify the steps of Solving Linear Equations

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

Content View

Student View

15 questions

Show all answers

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

VA.MATH.9-12.A.EI.1.a

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

VA.MATH.9-12.A.EI.1.b

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

VA.MATH.9-12.A.EI.1.a

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

VA.MATH.9-12.A.EI.1.b

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

VA.MATH.9-12.A.EI.1.a

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

VA.MATH.9-12.A.EI.1.b

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Tags

VA.MATH.9-12.A.EI.1.a

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

12 questions

Unit 7 Multiplication and Division Review

Quiz

•

3rd Grade - University

14 questions

Regents Prep

Quiz

•

9th Grade

20 questions

Pythagorean Theorem Practice

Quiz

•

7th - 9th Grade

20 questions

Parallelograms, Trapezoid, and Kite

Quiz

•

9th Grade

14 questions

Linear Equation in Two Variable Part-2

Quiz

•

9th Grade

10 questions

Arithmetic Properties

Quiz

•

9th Grade

20 questions

What is Arithmetic?

Quiz

•

7th - 9th Grade

10 questions

Limit CLass 9

Quiz

•

9th Grade

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

14 questions

Boundaries & Healthy Relationships

Lesson

•

6th - 8th Grade

13 questions

SMS Cafeteria Expectations Quiz

Quiz

•

6th - 8th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

12 questions

SMS Restroom Expectations Quiz

Quiz

•

6th - 8th Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

10 questions

Pi Day Trivia!

Quiz

•

6th - 9th Grade

Discover more resources for Mathematics

10 questions

Pi Day Trivia!

Quiz

•

6th - 9th Grade

15 questions

Pi Day Trivia!

Quiz

•

9th Grade

15 questions

Pi Day Trivia

Quiz

•

9th - 12th Grade

20 questions

Graphing Inequalities on a Number Line

Quiz

•

6th - 9th Grade

10 questions

Exploring Basic Probability Concepts

Interactive video

•

6th - 10th Grade

15 questions

Algebra 1 EOC Review #1

Quiz

•

9th Grade

11 questions

Adding and Subtracting Polynomials

Quiz

•

9th Grade

27 questions

Pi Day!

Quiz

•

6th - 9th Grade