What is |2x-5|<|3x-2| ?

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|2x-5|<|3x-2|

∣ 2 x - 5 ∣ < ∣ 3 x - 2 ∣

x < - 3 or x > \frac{7}{5}

Interval Notation

(- \infty, - 3) \cup (\frac{7}{5}, \infty)

Decimal Notation

x < - 3 or x > 1.4

Solution steps

∣ 2 x - 5 ∣ < ∣ 3 x - 2 ∣

Find positive and negative intervals

x < \frac{2}{3}, \frac{2}{3} \leq x < \frac{5}{2}, x \geq \frac{5}{2}

Solve the inequality for each interval

x < - 3 or \frac{7}{5} < x < \frac{5}{2} or x \geq \frac{5}{2}

Merge Overlapping Intervals

x < - 3 or x > \frac{7}{5}

∣ x - 7 ∣ \geq 2

(3 a^{2} b^{7}) (5 a^{3} b^{8})

a (n + 2) + n + 2

2 x^{2} + x - 9 = 0

\frac{x + 1}{x - 3} < 2