Question

Antoinette solves the linear equation 3 (x minus 3) + 2 x + 9 = 2 x + 2 (x minus 1) using the steps shown below.

Step 1: 3 x minus 3 + 2 x + 9 = 2 x + 2 (x minus 1)
Step 2: 5 x + 6 = 4 x minus 1
Step 3: 5 x minus 4 x = negative 1 minus 6
Step 4: x = negative 7

She checks her solution by substituting –7 for x in the original equation. She determines that her answer is incorrect. Which best describes Antoinette’s error?
She distributed incorrectly.
She incorrectly combined like terms.
She incorrectly applied the addition and subtraction properties of equality.
She incorrectly applied the multiplication and division properties of equality.

Answer 1

She distributed incorrectly.

Explanation:

In the first step,
`3(x-3)=3x-9`, not
`3x-3`.