Question

Analyzing Work
Caleb solved this equation and recorded his work.

7.4x + 4.1(2x − 4) = −2.3(x − 6) − 21.6

1. 7.4x + 8.2x − 16.4 = −2.3x + 13.8 − 21.6

2. 15.6x − 16.4 = −2.3x + 35.4

3. 17.9x − 16.4 = 35.4

4. 17.9x = 51.8

5. x ≈ 2.89

When Caleb verified his solution, it didn’t work. What mistake did he make?
In step 1, the distributive property was not used properly on the right side of the equation.
In step 2, the like terms were not combined properly on the right side of the equation.
In step 3, the addition property of equality was not used properly to isolate the variable term.
In step 5, the division property of equality was not used properly to solve for x.

Answer 1

In step 2 — the right-hand like terms were combined incorrectly. Caleb wrote 13.8 − 21.6 = 35.4, but 13.8 − 21.6 = −7.8.

Correct work:
7.4x + 4.1(2x − 4) = −2.3(x − 6) − 21.6
7.4x + 8.2x − 16.4 = −2.3x + 13.8 − 21.6
15.6x − 16.4 = −2.3x − 7.8
17.9x − 16.4 = −7.8
17.9x = 8.6
x = 8.6/17.9 ≈ 0.480.