What is |-3x+2|<x+6 ?

The solution to |-3x+2|<x+6 is -1<x<4

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|-3x+2|<x+6

∣ - 3 x + 2 ∣ < x + 6

- 1 < x < 4

Interval Notation

(- 1, 4)

Solution steps

∣ - 3 x + 2 ∣ < x + 6

Find positive and negative intervals

x \leq \frac{2}{3}, x > \frac{2}{3}

Solve the inequality for each interval

- 1 < x \leq \frac{2}{3} or \frac{2}{3} < x < 4

Merge Overlapping Intervals

- 1 < x < 4

4 < 7 - x

3 - \frac{9}{4}

- 2 z + 5.1 > - 16.5 + 4 z

2 x^{4} + 3 x^{3} - 6 x^{2} - 5 x + 6

- x + 9 > 9