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

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

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

∣ 2 x - 3 ∣ > ∣ x + 4 ∣

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

Interval Notation

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

Decimal Notation

x < - 0.33333 \dots or x > 7

Solution steps

∣ 2 x - 3 ∣ > ∣ x + 4 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

x < - 4 or - 4 \leq x < - \frac{1}{3} or x > 7

Merge Overlapping Intervals

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

∣ - 0.5 x ∣ < 1

[\frac{( x ^{2} - 5 x + 6 )}{( ∣ x ∣ + 7 )}] < 0

∣ 4 - 3 x ∣ - 2 > 0

∣ 3 x - 1 ∣ > 2 x

∣ 3 x - 2 ∣ \leq 4