What is (12}{x-1}-\frac{16)/x >= 4 ?

The solution to (12}{x-1}-\frac{16)/x >= 4 is -2<= x<0\lor 1<x<= 2

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(12}{x-1}-\frac{16)/x >= 4

\frac{12}{x - 1} - \frac{16}{x} \geq 4

- 2 \leq x < 0 or 1 < x \leq 2

Interval Notation

[- 2, 0) \cup (1, 2]

Solution steps

\frac{12}{x - 1} - \frac{16}{x} \geq 4

Rewrite in standard form

\frac{- 4 x ^{2} + 16}{x ( x - 1 )} \geq 0

Factor

\frac{- 4 x ^{2} + 16}{x ( x - 1 )} : \frac{- 4 ( x + 2 ) ( x - 2 )}{x ( x - 1 )}

\frac{- 4 ( x + 2 ) ( x - 2 )}{x ( x - 1 )} \geq 0

Multiply both sides by

- 1

(reverse the inequality)

\frac{( - 4 ( x + 2 ) ( x - 2 ) ) ( - 1 )}{x ( x - 1 )} \leq 0 \cdot (- 1)

Simplify

\frac{4 ( x + 2 ) ( x - 2 )}{x ( x - 1 )} \leq 0

Divide both sides by

4

\frac{\frac{4 ( x + 2 ) ( x - 2 )}{x ( x - 1 )}}{4} \leq \frac{0}{4}

Simplify

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

Identify the intervals

- 2 \leq x < 0 or 1 < x \leq 2

32 m^{2} - 4 m - 6 = 0

p (0) = 2 (0)^{3} + 4 (0)^{2} - 3

\frac{x}{- 3} - 7 = 14

- 3 + 2 x > 13

(x^{6})^{- \frac{1}{2}}

What is (12}{x-1}-\frac{16)/x >= 4 ?
The solution to (12}{x-1}-\frac{16)/x >= 4 is -2<= x<0\lor 1<x<= 2