Question

Peter solved an equation as shown below.

Given: minus left parenthesis 3x minus 2 right parenthesis plus 2 left parenthesis x minus 3 right parenthesis equals minus 7. Step 1 shows, minus 3x plus 2 plus 2x minus 6 equals minus 7. Step 2 shows, minus 3x plus 2x plus 2 minus 6 equals minus 7. Step 3 shows, minus x minus 4 equals minus 7. Step 4 shows, minus x minus 4 plus 4 equals -7 plus 4. Step 5 shows, minus x over -1 equals -3 over -1. Answer: x equals 3.

When did Peter apply the distributive property?

A.
from the given to step 1

B.
from step 1 to step 2

C.
from step 3 to step 4

D.
from step 4 to step 5

Answer 1

you sure?

Answer 2

Peter applied the distributive property in the transition from the given expression to step 1.

In step 1, he correctly distributed the negative sign and the 2 in the expression:

-(- (3x - 2)) becomes -3x + 2, and
- 2(x - 3) becomes 2x - 6.

Thus, the correct answer is:

**A. from the given to step 1**.

Answer 3

Let's take another look at the steps to clarify where the distributive property was applied.

1. **Given:** \(- (3x - 2) + 2(x - 3) = -7\)
2. **Step 1:** \(-3x + 2 + 2x - 6 = -7\)

In Step 1, Peter distributes the negative sign in front of the parenthesis containing \(3x - 2\) and also distributes the \(2\) in front of \(x - 3\). Therefore, this is indeed where the distributive property is applied.

3. **Step 2:** \(-3x + 2x + 2 - 6 = -7\) (this is just rearranging terms)
4. **Step 3:** \(-x - 4 = -7\) (combining like terms)
5. **Step 4:** \(-x - 4 + 4 = -7 + 4\) (adding 4 to both sides)
6. **Step 5:** \(-x / -1 = -3 / -1\) (dividing both sides by -1)

Taking this into account, my initial assessment holds true. The correct answer is:

**A. from the given to step 1.**

Thank you for prompting a reassessment!