What are the solutions to the absolute value equation |3X - 6| = 27?

To solve the absolute value equation |3X - 6| = 27, we start by recognizing that an absolute value equation |A| = B can be rewritten as two separate equations:

1. 3X - 6 = 27

2. 3X - 6 = -27

Now, we can solve each equation.

For the first equation (3X - 6 = 27):

• Add 6 to both sides:

3X = 27 + 6

3X = 33

• Divide both sides by 3:

X = 11

For the second equation (3X - 6 = -27):

• Again, add 6 to both sides:

3X = -27 + 6

3X = -21

• Divide both sides by 3:

X = -7

Thus, the solutions to the equation |3X - 6| = 27 are X = -7 and X = 11.

The correct choice contains these values, confirming that the solution set includes both X = -7 and X = 11.