What is ((x-12))/x <= (20)/(1-x) ?

The solution to ((x-12))/x <= (20)/(1-x) is -4<= x<=-3\lor 0<x<1

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((x-12))/x <= (20)/(1-x)

\frac{( x - 12 )}{x} \leq \frac{20}{1 - x}

- 4 \leq x \leq - 3 or 0 < x < 1

Interval Notation

[- 4, - 3] \cup (0, 1)

Solution steps

\frac{x - 12}{x} \leq \frac{20}{1 - x}

Rewrite in standard form

\frac{- x ^{2} - 7 x - 12}{x ( - x + 1 )} \leq 0

Factor

\frac{- x ^{2} - 7 x - 12}{x ( - x + 1 )} : \frac{- ( x + 3 ) ( x + 4 )}{x ( - x + 1 )}

\frac{- ( x + 3 ) ( x + 4 )}{x ( - x + 1 )} \leq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - ( x + 3 ) ( x + 4 ) ) ( - 1 )}{x ( - x + 1 )} \geq 0 \cdot (- 1)

Simplify

\frac{( x + 3 ) ( x + 4 )}{x ( - x + 1 )} \geq 0

Identify the intervals

- 4 \leq x \leq - 3 or 0 < x < 1

- 524

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t^{2} + 5 t + 6 = 0

4 y^{2} - 28 y + 49

x^{3} - 9 x^{2} + 18 x

What is ((x-12))/x <= (20)/(1-x) ?
The solution to ((x-12))/x <= (20)/(1-x) is -4<= x<=-3\lor 0<x<1