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

The most logical next step is to simplify the left side of the equation by combining like terms (5x and -2x). This simplifies the equation to 3x + 15 = 2x + 18, making it easier to isolate the variable in subsequent steps.

Question 2

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

Accepted Answer

y = 3

Answer

First, distribute the -4 to both terms inside the parentheses: 8y - 4y + 12 = 24. Next, combine like terms on the left side: 4y + 12 = 24. Then, subtract 12 from both sides: 4y = 12. Finally, divide both sides by 4 to find that 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

The formula for the perimeter of a rectangle is P = 2l + 2w. The length 'l' is given as 2w + 3. Substituting this into the perimeter formula gives 78 = 2(2w + 3) + 2w. Solving this equation: 78 = 4w + 6 + 2w, which simplifies to 78 = 6w + 6. Subtracting 6 gives 72 = 6w. Dividing by 6 gives w = 12 feet.

Question 4

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

Accepted Answer

x = 12

Answer

First, apply the distributive property on the left side: 4x - 5 = 3x + 7. Next, subtract 3x from both sides to gather the variable terms: x - 5 = 7. Finally, add 5 to both sides to isolate x: x = 12.

Question 5

Which of the following equations has no solution?

Accepted Answer

6(x + 1) = 6x - 2

Answer

To determine which equation has no solution, simplify each one. For 6(x + 1) = 6x - 2, distributing the 6 gives 6x + 6 = 6x - 2. If you subtract 6x from both sides, you get 6 = -2, which is a false statement. This indicates there is no value of x that will make the equation true, meaning it has no solution.

(LEAP) Louisiana Educational Assessment Program Practice Test

(LEAP) Louisiana Educational Assessment Program Practice Test

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