What is |2x-1|>|x+1|+2 ?

The solution to |2x-1|>|x+1|+2 is x 4

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|2x-1|>|x+1|+2

∣ 2 x - 1 ∣ > ∣ x + 1 ∣ + 2

x < - \frac{2}{3} or x > 4

Interval Notation

(- \infty, - \frac{2}{3}) \cup (4, \infty)

Decimal Notation

x < - 0.66666 \dots or x > 4

Solution steps

∣ 2 x - 1 ∣ > ∣ x + 1 ∣ + 2

Find positive and negative intervals

x < - 1, - 1 \leq x < \frac{1}{2}, x \geq \frac{1}{2}

Solve the inequality for each interval

x < - 1 or - 1 \leq x < - \frac{2}{3} or x > 4

Merge Overlapping Intervals

x < - \frac{2}{3} or x > 4

4 a^{2} b^{2} - 9 c^{2}

- 6 (x - 4)^{2} = - 54

5 k^{2} = 60 - 20 k

x^{2} - 12 x = - 23