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Popular >

2/(2-x)<= 4/x

Solution

\frac{2}{2 - x} \leq \frac{4}{x}

Solution

0 < x \leq \frac{4}{3} or x > 2

+2

Interval Notation

(0, \frac{4}{3}] \cup (2, \infty)

Decimal Notation

0 < x \leq 1.33333 \dots or x > 2

Solution steps

\frac{2}{2 - x} \leq \frac{4}{x}

Rewrite in standard form

\frac{6 x - 8}{x ( - x + 2 )} \leq 0

Factor

\frac{6 x - 8}{x ( - x + 2 )} : \frac{2 ( 3 x - 4 )}{x ( - x + 2 )}

\frac{2 ( 3 x - 4 )}{x ( - x + 2 )} \leq 0

Divide both sides by

2

\frac{\frac{2 ( 3 x - 4 )}{x ( - x + 2 )}}{2} \leq \frac{0}{2}

Simplify

\frac{3 x - 4}{x ( - x + 2 )} \leq 0

Identify the intervals

0 < x \leq \frac{4}{3} or x > 2

Popular Examples

simplify 14/51*3/4 simplify

\frac{14}{51} \cdot \frac{3}{4}

4 (2 x - 2) = 8

x^{2} = \frac{1}{9}

- x^{2} + 8 x + 4 = 0

factor 25k^2-4 factor

25 k^{2} - 4

Frequently Asked Questions (FAQ)

What is 2/(2-x)<= 4/x ?
The solution to 2/(2-x)<= 4/x is 0<x<= 4/3 \lor x>2