Final answer:
The correct series of steps reveals that x = -12, as the signs should have been distributed properly during the multiplication step.
Step-by-step explanation:
The student provided the following sequence of algebraic steps to solve an equation:
- -5x + 12 - 7x = -3(5x + 8)
- -5x + 12 - 7x = -15x + 24
- -12x + 12 = -15x + 24
- -12x + 12 = -15x + 24
- 3x + 12 = 24
- 3x = 12
- X = 4
However, there was a mistake made in the distribution step when multiplying -3 by each term in the parenthesis (5x + 8), which should result in -15x - 24, not -15x + 24. The mistake lies in the handling of the signs while distributing. Here's the corrected sequence:
- -5x + 12 - 7x = -3(5x + 8)
- -5x + 12 - 7x = -15x - 24
- -12x + 12 = -15x - 24
- Adding 15x to both sides: 3x + 12 = -24
- Subtracting 12 from both sides: 3x = -36
- Dividing both sides by 3: x = -12
Therefore, the correct answer is x = -12.