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

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

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|3-2x|<|x+4|

∣ 3 - 2 x ∣ < ∣ x + 4 ∣

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

Interval Notation

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

Decimal

- 0.33333 \dots < x < 7

Solution steps

∣ 3 - 2 x ∣ < ∣ x + 4 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

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

Merge Overlapping Intervals

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

6 x^{2} + x + 5 = 0

\frac{x - 8}{2 x + 9} \geq 1

6 x^{- 3}

6 x^{2} - x - 5 = 0

11 z + 30 z^{2} - 30