To choose the correct equations, let's examine each one.
A) \(-5x + 12 = 5x - 5\)
Rearranging gives: \(-5x - 5x = -5 - 12\) \(-10x = -17\) which simplifies to \(x = \frac{17}{10}\).
B) \(-5x + 12 = -5x - 12\)
Rearranging gives: \(-5x + 5x = -12 - 12\) \(0 = -24\) which is false.
C) \(-5x + 12 = 5x + 12\)
Rearranging gives: \(-5x - 5x = 12 - 12\) \(-10x = 0\) which simplifies to \(x = 0\).
D) \(-5x + 12 = -12x - 12\)
Rearranging gives: \(-5x + 12x = -12 - 12\) \(7x = -24\) which simplifies to \(x = -\frac{24}{7}\).
Proposed answers:
The following equations are valid:
- A) is true
- B) is false
- C) is true
- D) is true
So, the answers that apply are A, C, D.