Quiz about Justify the steps of Solving Linear Equations

Question 1

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.

Accepted Answer

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

Answer

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

Answer

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

Answer

$$x = 45 imes 3$$ , so $$x = 135$$

Question 2

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 3

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.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 4

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 5

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

Accepted Answer

$$8y = 56$$ , so $$y = 7$$

Answer

$$y + 8 = 56$$ , so $$y = 48$$

Answer

$$y = 56 imes 8$$ , so $$y = 448$$

Answer

$$8 + y = 56$$ , so $$y = 48$$

Question 6

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 7

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.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 8

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

Accepted Answer

All of the above

Answer

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

Answer

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

Answer

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

Question 9

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

Accepted Answer

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

Answer

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

Answer

$$x = 23 imes 12$$ , so $$x = 276$$

Answer

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

Question 10

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 11

The property used between step 1 and step 2 is

Accepted Answer

Inverse Property of addition

Answer

Substitution

Answer

Commutative Property of addition

Answer

Identity Property of addition

Question 12

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

Accepted Answer

Inverse Property of Addition

Answer

Associative Property of Addition

Answer

Zero Property

Answer

Identity Property of Addition

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