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

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

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

∣ 3 + 2 x ∣ < ∣ 4 - x ∣

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

Interval Notation

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

Decimal Notation

- 7 < x < 0.33333 \dots

Solution steps

∣ 3 + 2 x ∣ < ∣ 4 - x ∣

Find positive and negative intervals

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

Solve the inequality for each interval

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

Merge Overlapping Intervals

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

0 = 5 x^{2} + 2 x - 3

4 x \leq 4 (x + 15)

x y - 4 y + 4 x - 16

x - 4 = 0

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