What is |x+4|>|2x-3| ?

The solution to |x+4|>|2x-3| is -1/3 <x<7

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|x+4|>|2x-3|

∣ x + 4 ∣ > ∣ 2 x - 3 ∣

- \frac{1}{3} < x < 7

Interval Notation

(- \frac{1}{3}, 7)

Decimal Notation

- 0.33333 \dots < x < 7

Solution steps

∣ x + 4 ∣ > ∣ 2 x - 3 ∣

Find positive and negative intervals

x < - 4, - 4 \leq x < \frac{3}{2}, x \geq \frac{3}{2}

Solve the inequality for each interval

No Solution or - \frac{1}{3} < x < \frac{3}{2} or \frac{3}{2} \leq x < 7

Merge Overlapping Intervals

- \frac{1}{3} < x < 7

∣ 2 x - 3 ∣ > 20

∣ - 2 x + 1 ∣ \geq 4

\frac{1}{∣ x ∣ - 3} < \frac{1}{2}

x^{2} - 1 \leq 4

∣ x - 2 ∣ + ∣ x - 4 ∣ > 6