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

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Multiple Choice

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

Explanation:
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.

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
  1. 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.

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