LEAP - Louisiana Educational Assessment Program Solving Multi-Step Equations Questions and Answers

Question 1

A student is solving the equation 5(x + 3) - 2x = 2(x + 9).
The student's first step is to apply the distributive property, resulting in the equation 5x + 15 - 2x = 2x + 18.
Which of the following would be the most logical next step to solve for x?

Accepted Answer

Combine the like terms 5x and -2x on the left side of the equation.

Answer

Subtract 2x from both sides of the equation.

Answer

Add 2x to both sides of the equation.

Answer

Subtract 15 from both sides of the equation.

Question 2

Solve for y in the following equation: 8y - 4(y - 3) = 24.

Accepted Answer

y = 3

Answer

y = -9

Answer

y = 9

Answer

y = -3

Question 3

A rectangular garden has a perimeter of 78 feet. The length of the garden is 3 feet more than twice its width. If 'w' represents the width, which equation could be used to find the dimensions of the garden, and what is the correct width?

Accepted Answer

2(w) + 2(2w + 3) = 78; width = 12 feet

Answer

2(w) + 2(2w - 3) = 78; width = 14 feet

Answer

w + (2w + 3) = 78; width = 25 feet

Answer

2(w) + (2w + 3) = 78; width = 18.75 feet

Question 4

What is the solution to the equation 1/2(8x - 10) = 3x + 7?

Accepted Answer

x = 12

Answer

x = -2

Answer

x = 2

Answer

x = 1.5

Question 5

Which of the following equations has no solution?

Accepted Answer

6(x + 1) = 6x - 2

Answer

5x + 4 = 5(x + 0.8)

Answer

7(x - 2) = 7x - 14

Answer

3x - 8 = 2x - 8

Question 6

The sum of three consecutive odd integers is 141. If 'n' is the smallest of the three integers, which equation represents this situation and what is the value of n?

Accepted Answer

n + (n + 2) + (n + 4) = 141; n = 45

Answer

n + (n + 1) + (n + 2) = 141; n = 46

Answer

3n + 3 = 141; n = 46

Answer

3n = 141; n = 47