What is |x+3|>|2x-1| ?

The solution to |x+3|>|2x-1| is -2/3 <x<4

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|x+3|>|2x-1|

∣ x + 3 ∣ > ∣ 2 x - 1 ∣

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

Solution steps

∣ x + 3 ∣ > ∣ 2 x - 1 ∣

Find positive and negative intervals

x < - 3, - 3 \leq x < \frac{1}{2}, x \geq \frac{1}{2}

Solve the inequality for each interval

No Solution or - \frac{2}{3} < x < \frac{1}{2} or \frac{1}{2} \leq x < 4

Merge Overlapping Intervals

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

x^{2} + x - 5 < 0

∣ x - 2 ∣ > ∣ 2 x - 3 ∣

x^{2} - 7 x + 12 < ∣ x - 4 ∣

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

\frac{( x ^{2} - 3 x - 1 )}{( x ^{2} + x + 1 )} < 3