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

The solution to |(3-2x)/(2+x)| =-5/6

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

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

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

Interval Notation

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

Decimal Notation

x \leq - 5.5 or x \geq - 0.83333 \dots

Solution steps

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

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

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

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

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

Merge Overlapping Intervals

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

\frac{x}{4} + 10 = - 3

\frac{0}{1}

- 3 s \geq 33

6 = - s + 77

5 x^{2} + 11 x + 2

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