Question

An equation is shown below:

9(3x – 16) + 15 = 6x – 24
Part A: Write the steps you will use to solve the equation, and explain each step. (6 points)
Part B: What value of x makes the equation true? (4 points)

Answer 1

x = 5

Explanation:

Hello!

Step 1: Expand the left side by distributing

9(3x - 16) + 15 = 6x - 24

27x - 144 + 15 = 6x - 24

Step 2: Simplify the left side

27x - 144 + 15 = 6x - 24

27x - 129 = 6x - 24

Step 3: Subtract 6x from the both sides (collect like terms)

27x - 129 = 6x - 24

21x - 129 = -24

Step 4: Add 129 to both sides to isolate 21x (collect like terms)

21x - 129 = -24

21x = 105

Step 5: Divide both sides by 21 to isolate x

21x = 105

x = 5

What value of x makes this equation true? 5.

Answer 2

Part A

Given equation:

9(3x – 16) + 15 = 6x – 24

Expand the brackets:

⇒ 9(3x) + 9(-16) + 15 = 6x – 24

⇒ 27x - 144 + 15 = 6x – 24

Combine like terms:

⇒ 27x - 129 = 6x – 24

Subtract 6x from both sides:

⇒ 27x - 129 - 6x = 6x – 24 - 6x

⇒ 21x - 129 = -24

Add 129 to both sides:

⇒ 21x - 129 + 129 = -24 + 129

⇒ 21x = 105

Divide both sides by 21:

⇒ 21x ÷ 21 = 105 ÷ 21

⇒ x = 5

Part B

x = 5