Question

Solving Equations in Two Steps
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

Error in Step 2.

Work: 4b + 2b − 3 = −21 → 6b − 3 = −21 (Step 1 is correct).
To isolate 6b you must add 3 to both sides: 6b = −21 + 3 = −18 (not −24).
Then b = −18/6 = −3. (Step 3’s arithmetic would be correct if the previous line were −24, but that previous line is wrong.)