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Algebra · Absolute-Value

Solve Abs(2x + 1) = 3

\left|{2 x + 1}\right| = 3

Step by step

  1. \left|{2 x + 1}\right| = 3

    Start from the equation as given.

  2. \left|{2 x + 1}\right| - 3 = 0

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

  3. 2 x - 2 = 0 \Rightarrow x = 1

    Case 2 x + 1 non-negative: replace |2 x + 1| by (2 x + 1) and solve; keep only solutions consistent with that case.

  4. - 2 x - 4 = 0 \Rightarrow x = -2

    Case 2 x + 1 negative: replace |2 x + 1| by −(2 x + 1) and solve; keep only solutions consistent with that case.

Reveal the answer
x = 1 ,\; x = -2