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

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

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

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

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

Interval Notation

[- \frac{2}{3}, 4]

Decimal Notation

- 0.66666 \dots \leq x \leq 4

Solution steps

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

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

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

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

(x < - 3 or x \geq - \frac{2}{3}) and - 3 < x \leq 4

Merge Overlapping Intervals

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

∣ 3 x + 5 ∣ \leq \frac{7}{2}

\frac{1}{∣ x - 2 ∣} > 2

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

∣ 2 x - 5 ∣ \geq ∣ x + 2 ∣

∣ x ∣ \leq ∣ x + 1 ∣

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