What is |(x-2)/(3x+5)|<= 4 ?

The solution to |(x-2)/(3x+5)| =-18/13

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|(x-2)/(3x+5)|<= 4

\frac{x - 2}{3 x + 5} \leq 4

x \leq - 2 or x \geq - \frac{18}{13}

Interval Notation

(- \infty, - 2] \cup [- \frac{18}{13}, \infty)

Decimal Notation

x \leq - 2 or x \geq - 1.38461 \dots

Solution steps

\frac{x - 2}{3 x + 5} \leq 4

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 4 \leq \frac{x - 2}{3 x + 5} \leq 4

\frac{x - 2}{3 x + 5} \geq - 4 and \frac{x - 2}{3 x + 5} \leq 4

(x < - \frac{5}{3} or x \geq - \frac{18}{13}) and (x \leq - 2 or x > - \frac{5}{3})

Merge Overlapping Intervals

x \leq - 2 or x \geq - \frac{18}{13}

- \frac{1}{2} + 2

1 - e^{- \frac{π}{4} (\frac{5}{10})^{2}}

- 36 a^{2} + 9 a^{4}

3 - 2 x \leq - 5

\frac{2 x ^{- 3} y ^{- 2}}{z ^{4}}

What is |(x-2)/(3x+5)|<= 4 ?
The solution to |(x-2)/(3x+5)|<= 4 is x<=-2\lor x>=-18/13