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Popular >

3/(2-x)<= 1/x

Solution

\frac{3}{2 - x} \leq \frac{1}{x}

Solution

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

+2

Interval Notation

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

Decimal Notation

0 < x \leq 0.5 or x > 2

Solution steps

\frac{3}{2 - x} \leq \frac{1}{x}

Rewrite in standard form

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

Factor

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

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

Divide both sides by

2

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

Simplify

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

Identify the intervals

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

Popular Examples

u^{2} - 3 u = \frac{- 5}{4}

30 = - b + 23

- x^{2} + 81 x - 81 > 0

simplify (2-2i)^2 simplify

(2 - 2 i)^{2}

simplify (15a^3)/(3a)simplify

\frac{15 a ^{3}}{3 a}

Frequently Asked Questions (FAQ)

What is 3/(2-x)<= 1/x ?
The solution to 3/(2-x)<= 1/x is 0<x<= 1/2 \lor x>2