What is (|3x-1|)/(x+2)>-1 ?

The solution to (|3x-1|)/(x+2)>-1 is -2 1/3

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(|3x-1|)/(x+2)>-1

\frac{∣ 3 x - 1 ∣}{x + 2} > - 1

- 2 < x < \frac{1}{3} or x > \frac{1}{3}

Interval Notation

(- 2, \frac{1}{3}) \cup (\frac{1}{3}, \infty)

Decimal Notation

- 2 < x < 0.33333 \dots or x > 0.33333 \dots

Solution steps

\frac{∣ 3 x - 1 ∣}{x + 2} > - 1

Move

1

to the left side

\frac{∣ 3 x - 1 ∣}{x + 2} + 1 > 0

∣ 3 x - 1 ∣ \geq 0

\frac{a}{b} > 0 and a \geq 0

then

a > 0 and b > 0

∣ 3 x - 1 ∣ > 0 and (x + 2) > 0

∣ 3 x - 1 ∣ > 0 : x < \frac{1}{3} or x > \frac{1}{3}

x + 2 > 0 : x > - 2

Combine the intervals

(x < \frac{1}{3} or x > \frac{1}{3}) and x > - 2

Merge Overlapping Intervals

- 2 < x < \frac{1}{3} or x > \frac{1}{3}

8 - 3

\frac{x}{3} + 10 = 15

\frac{\frac{1}{6}}{\frac{1}{2}}

\frac{3}{10} + \frac{1}{5}

3 k^{2} + 15 k - 3

What is (|3x-1|)/(x+2)>-1 ?
The solution to (|3x-1|)/(x+2)>-1 is -2<x< 1/3 \lor x> 1/3