What is -(7x)/(x^2-100)>= (x+2)/(x+10) ?

The solution to -(7x)/(x^2-100)>= (x+2)/(x+10) is -10<x<=-4\lor 5<= x<10

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-(7x)/(x^2-100)>= (x+2)/(x+10)

- \frac{7 x}{x ^{2} - 100} \geq \frac{x + 2}{x + 10}

- 10 < x \leq - 4 or 5 \leq x < 10

Interval Notation

(- 10, - 4] \cup [5, 10)

Solution steps

- \frac{7 x}{x ^{2} - 100} \geq \frac{x + 2}{x + 10}

Rewrite in standard form

\frac{- x ^{2} + x + 20}{( x + 10 ) ( x - 10 )} \geq 0

Factor

\frac{- x ^{2} + x + 20}{( x + 10 ) ( x - 10 )} : \frac{- ( x + 4 ) ( x - 5 )}{( x + 10 ) ( x - 10 )}

\frac{- ( x + 4 ) ( x - 5 )}{( x + 10 ) ( x - 10 )} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 4 ) ( x - 5 ) ) ( - 1 )}{( x + 10 ) ( x - 10 )} \leq 0 \cdot (- 1)

Simplify

\frac{( x + 4 ) ( x - 5 )}{( x + 10 ) ( x - 10 )} \leq 0

Identify the intervals

- 10 < x \leq - 4 or 5 \leq x < 10

(- 2 + 3 i) \cdot (3 - i)

x^{2} + x + 25 = 0

1 \times (- 4) - 8 \times \frac{9}{- 3}

49 \cdot 3

4 x^{2} - 3 x + 6 = 0

What is -(7x)/(x^2-100)>= (x+2)/(x+10) ?
The solution to -(7x)/(x^2-100)>= (x+2)/(x+10) is -10<x<=-4\lor 5<= x<10