Question

Emeril solved this equation using the steps shown below:

4b + 2b – 3 = –21

1. Combine like terms: 6b − 3 = −21

2. Subtraction property of equality: 6b = −24

3. Subtraction property of equality: b = −4

Analyze the steps Emeril used to solve for the variable to determine if he made an error. In which step did Emeril make an error?
Step 1: He didn’t combine like terms correctly.
Step 2: He should have added 3 to, rather than subtracting 3 from, both sides.
Step 3: He should have gotten a positive answer when dividing -24 by 6.
There is no error.

Answer 1

Let's analyze each step of Emeril's solution.

1. **Combine like terms: 4b + 2b - 3 = -21**
- The combination of like terms is done correctly: \(4b + 2b = 6b\).
- This gives: **6b - 3 = -21** (This step is correct.)

2. **Subtraction property of equality: 6b = -24**
- To isolate \(6b\), Emeril subtracts \(3\) from both sides. However, on the left side, he should have added \(3\) to both sides.
- The correct operation would be:
\[
6b - 3 + 3 = -21 + 3 \implies 6b = -18.
\]
- Thus, this step contains an error.

3. **Subtraction property of equality: b = -4**
- Emeril divided \(-24\) by \(6\) to get \(b = -4\), but since the previous equation was incorrect, this step is also incorrect.

To summarize, **the error occurred in Step 2**, where Emeril incorrectly applied the operation of subtraction instead of addition. Therefore, the correct answer is:

**Step 2: He should have added 3 to, rather than subtracting 3 from, both sides.**