What is |x|+|x-2|>3 ?

The solution to |x|+|x-2|>3 is x 5/2

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|x|+|x-2|>3

∣ x ∣ + ∣ x - 2 ∣ > 3

x < - \frac{1}{2} or x > \frac{5}{2}

Interval Notation

(- \infty, - \frac{1}{2}) \cup (\frac{5}{2}, \infty)

Decimal Notation

x < - 0.5 or x > 2.5

Solution steps

∣ x ∣ + ∣ x - 2 ∣ > 3

Find positive and negative intervals

x < 0, 0 \leq x < 2, x \geq 2

Solve the inequality for each interval

x < - \frac{1}{2} or No Solution or x > \frac{5}{2}

Merge Overlapping Intervals

x < - \frac{1}{2} or x > \frac{5}{2}

∣ x ∣ < ∣ x + 1 ∣

∣ 2 x - 6 ∣ > x

\frac{( 2 x - 3 )}{5} \geq 3

∣ w + 7 ∣ > 2

\frac{∣ - 6 + p ∣}{8} > - 3