What is (36-x^2)/(x+6)>= 0 ?

The solution to (36-x^2)/(x+6)>= 0 is x<= 6

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(36-x^2)/(x+6)>= 0

\frac{36 - x ^{2}}{x + 6} \geq 0

x \leq 6

Interval Notation

(- \infty, 6]

Solution steps

\frac{36 - x ^{2}}{x + 6} \geq 0

Factor

\frac{36 - x ^{2}}{x + 6} : \frac{- ( x + 6 ) ( x - 6 )}{x + 6}

\frac{- ( x + 6 ) ( x - 6 )}{x + 6} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 6 ) ( x - 6 ) ) ( - 1 )}{x + 6} \leq 0 \cdot (- 1)

Simplify

\frac{( - ( x + 6 ) ( x - 6 ) ) ( - 1 )}{x + 6} : x - 6

x - 6 \leq 0

Identify the intervals

x \leq 6

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