What is |(2-3x)/(1+2x)|<= 4 ?

The solution to |(2-3x)/(1+2x)| =-2/11

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|(2-3x)/(1+2x)|<= 4

\frac{2 - 3 x}{1 + 2 x} \leq 4

x \leq - \frac{6}{5} or x \geq - \frac{2}{11}

Interval Notation

(- \infty, - \frac{6}{5}] \cup [- \frac{2}{11}, \infty)

Decimal Notation

x \leq - 1.2 or x \geq - 0.18181 \dots

Solution steps

\frac{2 - 3 x}{1 + 2 x} \leq 4

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- 4 \leq \frac{2 - 3 x}{1 + 2 x} \leq 4

\frac{2 - 3 x}{1 + 2 x} \geq - 4 and \frac{2 - 3 x}{1 + 2 x} \leq 4

(x \leq - \frac{6}{5} or x > - \frac{1}{2}) and (x < - \frac{1}{2} or x \geq - \frac{2}{11})

Merge Overlapping Intervals

x \leq - \frac{6}{5} or x \geq - \frac{2}{11}

\frac{3 + 4 i}{4 - 2 i}

3 (72 - 32)

3 x + 2 < - 13

\frac{12 a ^{- 3} b ^{10}}{- 3 a ^{- 7} b ^{- 2}}

\frac{8 v}{28 w + 21} - \frac{3 v + 10}{4 w + 3}

What is |(2-3x)/(1+2x)|<= 4 ?
The solution to |(2-3x)/(1+2x)|<= 4 is x<=-6/5 \lor x>=-2/11