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

The solution to |(x+2)/(3x-1)|>= 1 is -1/4 <= x< 1/3 \lor 1/3 <x<= 3/2

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

\frac{x + 2}{3 x - 1} \geq 1

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

Interval Notation

[- \frac{1}{4}, \frac{1}{3}) \cup (\frac{1}{3}, \frac{3}{2}]

Decimal Notation

- 0.25 \leq x < 0.33333 \dots or 0.33333 \dots < x \leq 1.5

Solution steps

\frac{x + 2}{3 x - 1} \geq 1

Apply absolute rule: If

∣ u ∣ \geq a, a > 0

then

u \leq - a

u \geq a

\frac{x + 2}{3 x - 1} \leq - 1 or \frac{x + 2}{3 x - 1} \geq 1

\frac{x + 2}{3 x - 1} \leq - 1 or \frac{x + 2}{3 x - 1} \geq 1

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

(x - 4) (x + 6) - (x - 3)^{2} = 15

9^{2} + 4 0^{2}

∣ 3 a + 4 ∣ = ∣ 4 a - 10 ∣

x^{3} y^{3} + 343

\frac{3 + 5 x}{5} = \frac{4 - x}{8}

What is |(x+2)/(3x-1)|>= 1 ?
The solution to |(x+2)/(3x-1)|>= 1 is -1/4 <= x< 1/3 \lor 1/3 <x<= 3/2