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Algebra · Absolute-Value

Solve Abs(3x - 2) = 4

\left|{3 x - 2}\right| = 4

Step by step

  1. \left|{3 x - 2}\right| = 4

    Start from the equation as given.

  2. \left|{3 x - 2}\right| - 4 = 0

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

  3. 3 x - 6 = 0 \Rightarrow x = 2

    Case 3 x - 2 non-negative: replace |3 x - 2| by (3 x - 2) and solve; keep only solutions consistent with that case.

  4. - 3 x - 2 = 0 \Rightarrow x = - \frac{2}{3}

    Case 3 x - 2 negative: replace |3 x - 2| by −(3 x - 2) and solve; keep only solutions consistent with that case.

Reveal the answer
x = 2 ,\; x = - \frac{2}{3}