What is |3x-1|<2x+5 ?

The solution to |3x-1|<2x+5 is -4/5 <x<6

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|3x-1|<2x+5

∣ 3 x - 1 ∣ < 2 x + 5

- \frac{4}{5} < x < 6

Interval Notation

(- \frac{4}{5}, 6)

Decimal Notation

- 0.8 < x < 6

Solution steps

∣ 3 x - 1 ∣ < 2 x + 5

Find positive and negative intervals

x < \frac{1}{3}, x \geq \frac{1}{3}

Solve the inequality for each interval

- \frac{4}{5} < x < \frac{1}{3} or \frac{1}{3} \leq x < 6

Merge Overlapping Intervals

- \frac{4}{5} < x < 6

12 (x + 5) = 4 x

2 + 4 z \geq 10

4 n - 5 = 23

- 3 x (2 - x) + 5 (x - 2)^{2}

2 \cdot 5 + 1 + 5 = 8