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

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Study for the BMS Mathematics Academic Team Test. Prepare with flashcards and multiple choice questions, each with hints and explanations. Elevate your math skills and ace your exam!

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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