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

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

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

∣ 2 x + 3 ∣ < ∣ x - 2 ∣

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

Interval Notation

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

Decimal Notation

- 5 < x < - 0.33333 \dots

Solution steps

∣ 2 x + 3 ∣ < ∣ x - 2 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

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

Merge Overlapping Intervals

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

5 - 2 t = 3 t

8 \cdot 20

- 7 (n + 2) = - 14 - 7 n

\frac{13 !}{6 ! ( 13 - 6 ) !}

- 2 x = 12