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

The solution to |(3x-2)/(2x+1)|<= 1 is 1/5 <= x<= 3

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

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

\frac{1}{5} \leq x \leq 3

Interval Notation

[\frac{1}{5}, 3]

Decimal Notation

0.2 \leq x \leq 3

Solution steps

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

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

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

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

(x < - \frac{1}{2} or x \geq \frac{1}{5}) and - \frac{1}{2} < x \leq 3

Merge Overlapping Intervals

\frac{1}{5} \leq x \leq 3

0.4 x + 1.4 - 0.7 x = 10.4

\frac{π}{4} \cdot 2

4 m + 6 < 2

y^{2} - 4

What is |(3x-2)/(2x+1)|<= 1 ?
The solution to |(3x-2)/(2x+1)|<= 1 is 1/5 <= x<= 3