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What is the solution to the equation |x - 3| = 5?

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Question: What is the solution to the equation |x - 3| = 5?

Options:

  1. {8, -2}
  2. {3, 5}
  3. {5, 1}
  4. {0, 6}

Correct Answer: {8, -2}

Solution: 

The absolute value equation gives two cases: x - 3 = 5 or x - 3 = -5, leading to x = 8 or x = -2.

What is the solution to the equation |x - 3| = 5?

Practice Questions

Q1
What is the solution to the equation |x - 3| = 5?
  1. {8, -2}
  2. {3, 5}
  3. {5, 1}
  4. {0, 6}

Questions & Step-by-Step Solutions

What is the solution to the equation |x - 3| = 5?
  • Step 1: Understand that |x - 3| means the distance of (x - 3) from 0.
  • Step 2: Set up two separate equations because the absolute value can be positive or negative.
  • Step 3: First equation: x - 3 = 5. Solve for x by adding 3 to both sides: x = 5 + 3, which gives x = 8.
  • Step 4: Second equation: x - 3 = -5. Solve for x by adding 3 to both sides: x = -5 + 3, which gives x = -2.
  • Step 5: The solutions to the equation |x - 3| = 5 are x = 8 and x = -2.
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