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Popular >

3/((2-x))<= 1/((x+4))

Solution

\frac{3}{( 2 - x )} \leq \frac{1}{( x + 4 )}

Solution

- 4 < x \leq - \frac{5}{2} or x > 2

+2

Interval Notation

(- 4, - \frac{5}{2}] \cup (2, \infty)

Decimal Notation

- 4 < x \leq - 2.5 or x > 2

Solution steps

\frac{3}{2 - x} \leq \frac{1}{x + 4}

Rewrite in standard form

\frac{4 x + 10}{( - x + 2 ) ( x + 4 )} \leq 0

Factor

\frac{4 x + 10}{( - x + 2 ) ( x + 4 )} : \frac{2 ( 2 x + 5 )}{( - x + 2 ) ( x + 4 )}

\frac{2 ( 2 x + 5 )}{( - x + 2 ) ( x + 4 )} \leq 0

Divide both sides by

2

\frac{\frac{2 ( 2 x + 5 )}{( - x + 2 ) ( x + 4 )}}{2} \leq \frac{0}{2}

Simplify

\frac{2 x + 5}{( - x + 2 ) ( x + 4 )} \leq 0

Identify the intervals

- 4 < x \leq - \frac{5}{2} or x > 2

Popular Examples

((2x-1))/((x+1))>= 6

\frac{( 2 x - 1 )}{( x + 1 )} \geq 6

x^{2} - 9 x + 8 \leq 0

(x + 4)^{2} > 0

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

\frac{x}{( x - 3 )} \leq \frac{1}{x}

(x+3)^{553}*(3x-2)^{555}*(7-x)^{343}<0

(x + 3)^{553} \cdot (3 x - 2)^{555} \cdot (7 - x)^{343} < 0

Frequently Asked Questions (FAQ)

What is 3/((2-x))<= 1/((x+4)) ?
The solution to 3/((2-x))<= 1/((x+4)) is -4<x<=-5/2 \lor x>2