Question

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

Step 1: 3x-3+2x+9 = 2x+ 2x-
Step 2: 5x+6= 4x-1
Step 3: 5x-4x=-1-6
Step 4: X=-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

A

Explanation:

Answer 2

Antoinette's error

Option A) She distributed incorrectly.

Explanation:

We are given the following information in the question:

Antoinette solves the linear equation

`3(x-3)+2x+9 = 2x+ 2(x-1)`

Antoinette made mistake in step 1 that is she did not distributed correctly.

If she would have distributed correctly, then she would have got the following solution:

`3(x-3)+2x+9 = 2x+ 2(x-1)\\\text{Step 1: }3x-9+2x+9 = 2x + 2x-2\\\text{Step 2: }5x = 4x -1\\\text{Step 3: }5x-4x = -1\\\text{Step 4: }x = -1`

Substituting x = -1 in the given equation, we gwt:

`3(-1-3)+2(-1)+9 = 2(-1)+ 2(-1-1)\\-12-2+9 = -2-4\\-6=-6\\\text{which is true}`

Antoinette's error

Option A) She distributed incorrectly.