Find all real solutions to the equation |2*x - 3| = |x + 6|.

Answer and explanation

Correct answer: C. x = 9 and x = -1

  1. Step 1: Case 1: 2*x - 3 = x + 6. Subtract x: x - 3 = 6, so x = 9.
  2. Step 2: Case 2: 2x - 3 = -(x + 6) = -x - 6. Add x: 3x - 3 = -6, so 3*x = -3, giving x = -1.
  3. Step 3: Check both in original equation: |2(9) - 3| = 15 and |9 + 6| = 15; |2(-1) - 3| = 5 and |-1 + 6| = 5. Both hold.
Answer
x = 9 and x = -1.
Why not the others: x = 9 only omits the negative branch root; x = 3 gives |3| != |9|; x = 6 gives |9| != |12|.

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