What is 8/(2-x)>= x/(x-2)+1 ?

The solution to 8/(2-x)>= x/(x-2)+1 is -3<= x<2

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8/(2-x)>= x/(x-2)+1

\frac{8}{2 - x} \geq \frac{x}{x - 2} + 1

- 3 \leq x < 2

Solution steps

\frac{8}{2 - x} \geq \frac{x}{x - 2} + 1

Rewrite in standard form

\frac{2 x ^{2} + 2 x - 12}{( - x + 2 ) ( x - 2 )} \geq 0

Factor

\frac{2 x ^{2} + 2 x - 12}{( - x + 2 ) ( x - 2 )} : \frac{2 ( x - 2 ) ( x + 3 )}{( - x + 2 ) ( x - 2 )}

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

Divide both sides by

2

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

Simplify

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

Identify the intervals

- 3 \leq x < 2

\frac{2}{3} + \frac{1}{6}

x + 5 \leq 5 or x + 5 \geq 6

- 3 p + 700 = 2 p - 500

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