Emeril solved this equation using the steps shown below:

Question

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.