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

The solution to (3x-4)/(2x+4)<= 1 is -2<x<= 8

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

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

- 2 < x \leq 8

Solution steps

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

Rewrite in standard form

\frac{x - 8}{2 x + 4} \leq 0

Factor

\frac{x - 8}{2 x + 4} : \frac{x - 8}{2 ( x + 2 )}

\frac{x - 8}{2 ( x + 2 )} \leq 0

Multiply both sides by

2

\frac{2 ( x - 8 )}{2 ( x + 2 )} \leq 0 \cdot 2

Simplify

\frac{x - 8}{x + 2} \leq 0

Identify the intervals

- 2 < x \leq 8

3 x \geq 8

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