Question

Look at the sample work below: \(2x - 8 = 12\). \(\frac{1}{2}(2x - 8) = \frac{1}{2}(12)\). \(x - 8 = 6\). \(x - 8 + 8 = 6 + 8\). \(x = 14\). Which error, if any, was made?

- A. The substitution property of equality was not applied correctly.
- B. The addition property of equality was not applied correctly.
- C. The multiplication property of equality was not applied correctly.
- D. No errors were made.

Answer 1

The mistake in the equation 2x - 8 = 12 was incorrectly applying the multiplication property of equality. The proper application involves multiplying or dividing each term on both sides of the equation. The error corresponds to option C.

Step-by-step explanation:

In the provided sample work of solving the equation 2x - 8 = 12, a mistake occurs at the step: ½(2x - 8) = ½(12). The error is in the application of the multiplication property of equality. When multiplying or dividing both sides of an equation by a number, it is essential to apply it to every term on both sides of the equation. The correct application would be ½ × 2x - ½ × 8 = ½ × 12, simplifying to x - 4 = 6. Therefore, the answer to the multiple-choice question is C. The multiplication property of equality was not applied correctly.