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Algebra · Absolute-Value

Solve Abs(x - 2) = 5

\left|{x - 2}\right| = 5

Step by step

  1. \left|{x - 2}\right| = 5

    Start from the equation as given.

  2. \left|{x - 2}\right| - 5 = 0

    Split into the two cases inside the absolute value: positive and negative.

  3. x - 7 = 0 \Rightarrow x = 7

    Case x - 2 non-negative: replace |x - 2| by (x - 2) and solve; keep only solutions consistent with that case.

  4. - x - 3 = 0 \Rightarrow x = -3

    Case x - 2 negative: replace |x - 2| by −(x - 2) and solve; keep only solutions consistent with that case.

Reveal the answer
x = 7 ,\; x = -3