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

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

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|3x-1|<|2+2x|

∣ 3 x - 1 ∣ < ∣ 2 + 2 x ∣

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

Interval Notation

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

Decimal Notation

- 0.2 < x < 3

Solution steps

∣ 3 x - 1 ∣ < ∣ 2 + 2 x ∣

Find positive and negative intervals

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

Solve the inequality for each interval

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

Merge Overlapping Intervals

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

5 \leq 3 x - 7 \leq 17

ln (17) = x

- 1 = 5 b - 6 b

∣ 4 - 2 x ∣ \leq 6

\frac{1}{2} - 3