What is 8/(5(x+3/4))>(4/9-1/3)*(-6/5 x) ?

The solution to 8/(5(x+3/4))>(4/9-1/3)*(-6/5 x) is x>-3/4

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8/(5(x+3/4))>(4/9-1/3)*(-6/5 x)

\frac{8}{5 ( x + \frac{3}{4} )} > (\frac{4}{9} - \frac{1}{3}) \cdot (- \frac{6}{5} x)

x > - \frac{3}{4}

Interval Notation

(- \frac{3}{4}, \infty)

Decimal Notation

x > - 0.75

Solution steps

\frac{8}{5 ( x + \frac{3}{4} )} > (\frac{4}{9} - \frac{1}{3}) (- \frac{6}{5} x)

Rewrite in standard form

\frac{288 + 6 x ( 4 x + 3 )}{4 x + 3} > 0

Factor

\frac{288 + 6 x ( 4 x + 3 )}{4 x + 3} : \frac{6 ( 4 x ^{2} + 3 x + 48 )}{4 x + 3}

\frac{6 ( 4 x ^{2} + 3 x + 48 )}{4 x + 3} > 0

Divide both sides by

6

\frac{\frac{6 ( 4 x ^{2} + 3 x + 48 )}{4 x + 3}}{6} > \frac{0}{6}

Simplify

\frac{4 x ^{2} + 3 x + 48}{4 x + 3} > 0

Identify the intervals

x > - \frac{3}{4}

\frac{3 x + 54}{( 2 x + 3 )} \leq 18

3 x^{2} (x - 4)^{2} < 32 - 5 (x - 2)^{2}

x^{2} - 18 > 0

2 x^{2} + 3 x < 4

\frac{4}{( x - 2 )} > \frac{3}{( x + 5 )}

What is 8/(5(x+3/4))>(4/9-1/3)*(-6/5 x) ?
The solution to 8/(5(x+3/4))>(4/9-1/3)*(-6/5 x) is x>-3/4