What is (x^2-35)/(x+7)>= x ?

The solution to (x^2-35)/(x+7)>= x is -7<x<=-5

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(x^2-35)/(x+7)>= x

\frac{x ^{2} - 35}{x + 7} \geq x

- 7 < x \leq - 5

Interval Notation

(- 7, - 5]

Solution steps

\frac{x ^{2} - 35}{x + 7} \geq x

Rewrite in standard form

\frac{- 7 x - 35}{x + 7} \geq 0

Factor

\frac{- 7 x - 35}{x + 7} : \frac{- 7 ( x + 5 )}{x + 7}

\frac{- 7 ( x + 5 )}{x + 7} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 7 ( x + 5 ) ) ( - 1 )}{x + 7} \leq 0 \cdot (- 1)

Simplify

\frac{7 ( x + 5 )}{x + 7} \leq 0

Divide both sides by

7

\frac{\frac{7 ( x + 5 )}{x + 7}}{7} \leq \frac{0}{7}

Simplify

\frac{x + 5}{x + 7} \leq 0

Identify the intervals

- 7 < x \leq - 5

\frac{8 x}{3} - \frac{3 x}{3} = \frac{10}{2}

\frac{- 2}{1 - x} < 9

(5 - i 3) (1 + i 3)

2 0^{\frac{1}{2}}