What is (2x+3)/(15-5x)>= 0 ?

The solution to (2x+3)/(15-5x)>= 0 is -3/2 <= x<3

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(2x+3)/(15-5x)>= 0

\frac{2 x + 3}{15 - 5 x} \geq 0

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

Solution steps

\frac{2 x + 3}{15 - 5 x} \geq 0

Factor

\frac{2 x + 3}{15 - 5 x} : \frac{2 x + 3}{- 5 ( x - 3 )}

\frac{2 x + 3}{- 5 ( x - 3 )} \geq 0

Simplify

\frac{2 x + 3}{- 5 ( x - 3 )} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( 2 x + 3 ) ( - 1 )}{- 5 ( x - 3 )} \leq 0 \cdot (- 1)

Simplify

\frac{2 x + 3}{5 ( x - 3 )} \leq 0

Multiply both sides by

5

\frac{5 ( 2 x + 3 )}{5 ( x - 3 )} \leq 0 \cdot 5

Simplify

\frac{2 x + 3}{x - 3} \leq 0

Identify the intervals

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

- 5 u^{2} + 13 u - 6

\frac{x ^{3} y ^{4} x ^{- 2} y ^{- 5}}{y ^{3} x ^{5} y ^{- 2}}

5 (x^{2} - 1) > 24 x

- 33 > 6 a + 3

- 4 \leq 6 - 2 x < 4