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

The solution to |((3x))/(2+5)|<= 2 is -14/3 <= x<= 14/3

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

\frac{( 3 x )}{2 + 5} \leq 2

- \frac{14}{3} \leq x \leq \frac{14}{3}

Solution steps

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

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

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

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

x \geq - \frac{14}{3} and x \leq \frac{14}{3}

Merge Overlapping Intervals

- \frac{14}{3} \leq x \leq \frac{14}{3}

\frac{( x + 4 )}{( x + 2 )} \leq 1

∣ x + 4 ∣ > ∣ 2 x - 3 ∣

∣ 2 x - 3 ∣ > 20

∣ - 2 x + 1 ∣ \geq 4

\frac{1}{∣ x ∣ - 3} < \frac{1}{2}

What is |((3x))/(2+5)|<= 2 ?
The solution to |((3x))/(2+5)|<= 2 is -14/3 <= x<= 14/3