What is 4/(5-3x)<=-1 ?

The solution to 4/(5-3x)<=-1 is 5/3 <x<= 3

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4/(5-3x)<=-1

\frac{4}{5 - 3 x} \leq - 1

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

Solution steps

\frac{4}{5 - 3 x} \leq - 1

Rewrite in standard form

\frac{- 3 x + 9}{5 - 3 x} \leq 0

Factor

\frac{- 3 x + 9}{5 - 3 x} : \frac{- 3 ( x - 3 )}{5 - 3 x}

\frac{- 3 ( x - 3 )}{5 - 3 x} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 3 ( x - 3 ) ) ( - 1 )}{5 - 3 x} \geq 0 \cdot (- 1)

Simplify

\frac{3 ( x - 3 )}{5 - 3 x} \geq 0

Divide both sides by

3

\frac{\frac{3 ( x - 3 )}{5 - 3 x}}{3} \geq \frac{0}{3}

Simplify

\frac{x - 3}{5 - 3 x} \geq 0

Identify the intervals

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

r^{2} + 9 r + 14

5 x \leq 30

b^{2} - a^{2}

- \frac{4}{5} - \frac{2}{3} (y - 9) \geq \frac{3}{5} (y + 15)

\frac{4}{3} - 2