Question

A student claims that 8x - 2(4+3x) is equivalent to 3x. The student steps are shown below.

Expression: 8x - 2(4+3x)
Step 1: 8x - 8 + 3x
Step 2: 8x + 3x - 8
Step 3:11x - 8
Step 4: 3x

Answer 1

The student’s claim is incorrect. Let’s evaluate the expression step by step to see why:

8x - 2(4+3x) = 8x - 8 - 6x

= 2x - 8

Explanation:

As we can see, the expression 8x - 2(4+3x) simplifies to 2x - 8, not 3x. Therefore, the student’s claim is incorrect.

Answer 2

A) Distributive property error in step 1.

B) 2x - 8

Explanation:

The student initially made an error in step 1. In this step, the student did not correctly distribute -2 to the second term (3x) inside the parentheses. This is a distributive property error. This initial error affected each of the following steps in the calculation, making them incorrect.

The distributive property states that when you multiply a number outside the parentheses by the sum or difference inside the parentheses, you must distribute that number to each term inside the parentheses. Therefore, the correct calculation is:

`\begin{aligned}\textsf{Expression:} \quad & 8x - 2(4 + 3x)\\\textsf{Step 1:} \quad & 8x - 8 - 6x\\\textsf{Step 2:} \quad & 8x -6x - 8\\\textsf{Step 3:} \quad & 2x - 8\end{aligned}`

So, the final simplified expression is 2x - 8.