What is ((x+5))/((20-5x))>= 0 ?

The solution to ((x+5))/((20-5x))>= 0 is -5<= x<4

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((x+5))/((20-5x))>= 0

\frac{( x + 5 )}{( 20 - 5 x )} \geq 0

- 5 \leq x < 4

Interval Notation

[- 5, 4)

Solution steps

\frac{x + 5}{20 - 5 x} \geq 0

Factor

\frac{x + 5}{20 - 5 x} : \frac{x + 5}{- 5 ( x - 4 )}

\frac{x + 5}{- 5 ( x - 4 )} \geq 0

Simplify

\frac{x + 5}{- 5 ( x - 4 )} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( x + 5 ) ( - 1 )}{- 5 ( x - 4 )} \leq 0 \cdot (- 1)

Simplify

\frac{x + 5}{5 ( x - 4 )} \leq 0

Multiply both sides by

5

\frac{5 ( x + 5 )}{5 ( x - 4 )} \leq 0 \cdot 5

Simplify

\frac{x + 5}{x - 4} \leq 0

Identify the intervals

- 5 \leq x < 4

x^{2} x > 0

x^{2} - 6 x - 16 \leq 0

\frac{( 9 - x ^{2} )}{x} > 0

3 x^{2} - 11 x + 2 < 0

12 - (x^{2} - 101) < - 74 + 6 x^{2}

What is ((x+5))/((20-5x))>= 0 ?
The solution to ((x+5))/((20-5x))>= 0 is -5<= x<4