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

The solution to 1/(2x)>= ((x+2))/(x-1) is -1<= x<=-1/2 \lor 0<x<1

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

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

- 1 \leq x \leq - \frac{1}{2} or 0 < x < 1

Interval Notation

[- 1, - \frac{1}{2}] \cup (0, 1)

Decimal Notation

- 1 \leq x \leq - 0.5 or 0 < x < 1

Solution steps

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

Rewrite in standard form

\frac{- 2 x ^{2} - 3 x - 1}{x ( x - 1 )} \geq 0

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

- 1 \leq x \leq - \frac{1}{2} or 0 < x < 1

\frac{1}{2} (0.2)

∣ 7 ∣

i^{29}

- x^{2} + 25 x - 100 > 0

6 (2 y - 2) = 36

What is 1/(2x)>= ((x+2))/(x-1) ?
The solution to 1/(2x)>= ((x+2))/(x-1) is -1<= x<=-1/2 \lor 0<x<1