What is 3/(2x+5)-x>0 ?

The solution to 3/(2x+5)-x>0 is x<-3\lor-5/2 <x< 1/2

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3/(2x+5)-x>0

\frac{3}{2 x + 5} - x > 0

x < - 3 or - \frac{5}{2} < x < \frac{1}{2}

Solution steps

\frac{3}{2 x + 5} - x > 0

Rewrite in standard form

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

Factor

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

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

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

x < - 3 or - \frac{5}{2} < x < \frac{1}{2}

(x^{2}) (x^{- \frac{1}{2}})

\frac{2 a - 3}{3} = \frac{4 a + 2}{4}

x^{2} + 7 x + 10 \leq 0

\frac{2 x ^{2}}{3} - x < \frac{8 x}{3} (1 + x) + 1

3 r - 6 = 18