What is 1/((2x-3))<= 1/((2x+5)) ?

The solution to 1/((2x-3))<= 1/((2x+5)) is -5/2 <x< 3/2

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1/((2x-3))<= 1/((2x+5))

\frac{1}{( 2 x - 3 )} \leq \frac{1}{( 2 x + 5 )}

- \frac{5}{2} < x < \frac{3}{2}

Interval Notation

(- \frac{5}{2}, \frac{3}{2})

Decimal Notation

- 2.5 < x < 1.5

Solution steps

\frac{1}{2 x - 3} \leq \frac{1}{2 x + 5}

Rewrite in standard form

\frac{1}{( 2 x - 3 ) ( 2 x + 5 )} \leq 0

\frac{1}{a} \leq 0

then

a < 0

(2 x - 3) (2 x + 5) < 0

Identify the intervals

- \frac{5}{2} < x < \frac{3}{2}

\frac{( x - 4 ) ^{2}}{x} > 0

\frac{( 2 x - 7 )}{( x - 5 )} \leq 3

\frac{( ( x - 7 - x ^{2} ) ( x ^{2} + 6 ) )}{( x ^{2} - x - 1 )} \leq 0

x (x^{2} - x) (x^{3} - x) (x^{4} - x) < 0

x^{4} - 2 x^{2} + 3 > x^{3} + 3

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