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

The solution to |2x-1|<|x+1| is 0<x<2

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|2x-1|<|x+1|

∣ 2 x - 1 ∣ < ∣ x + 1 ∣

0 < x < 2

Solution steps

∣ 2 x - 1 ∣ < ∣ x + 1 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or 0 < x < \frac{1}{2} or \frac{1}{2} \leq x < 2

Merge Overlapping Intervals

0 < x < 2

7 x^{2} - 7 x + 12 < ∣ x - 4 ∣

\frac{( x - 1 )}{( 2 - x )} > 0

x^{2} + 3 x + x^{2} - 2 > 0

∣ x - 4 ∣ > ∣ 2 x - 3 ∣

2^{4} x^{2} - 1 - 5 \geq 3