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

The solution to |2x-3|<|x+2| is 1/3 <x<5

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|2x-3|<|x+2|

∣ 2 x - 3 ∣ < ∣ x + 2 ∣

\frac{1}{3} < x < 5

Interval Notation

(\frac{1}{3}, 5)

Decimal Notation

0.33333 \dots < x < 5

Solution steps

∣ 2 x - 3 ∣ < ∣ x + 2 ∣

Find positive and negative intervals

x < - 2, - 2 \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 < 5

Merge Overlapping Intervals

\frac{1}{3} < x < 5

x^{2} - 3 x + 1 < 1

∣ 2 x - 1 ∣ + ∣ x ∣ \leq 10

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

∣ x - 3 ∣ - ∣ x - 3 ∣ - ∣ x + 4 ∣ \leq 10

\frac{( x - 3 )}{( x + 1 )} \leq 1