Solve (5/2x)div3/2+(15/4x)div(-9/8)<-frac{1}{6}

$$( \frac{ 5 }{ 2 } x) \div \frac{ 3 }{ 2 } +( \frac{ 15 }{ 4 } x) \div (- \frac{ 9 }{ 8 } ) < - \frac{ 1 }{ 6 }$$

Solve for x

$$x>\frac{1}{10}$$

Solution Steps

Divide \frac{5}{2}x by \frac{3}{2} to get \frac{5}{3}x.

$$\frac{5}{3}x+\frac{\frac{15}{4}x}{-\frac{9}{8}}<-\frac{1}{6}$$

Divide \frac{15}{4}x by -\frac{9}{8} to get -\frac{10}{3}x.

$$\frac{5}{3}x-\frac{10}{3}x<-\frac{1}{6}$$

Combine \frac{5}{3}x and -\frac{10}{3}x to get -\frac{5}{3}x.

$$-\frac{5}{3}x<-\frac{1}{6}$$

Multiply both sides by -\frac{3}{5}, the reciprocal of -\frac{5}{3}. Since -\frac{5}{3} is negative, the inequality direction is changed.

$$x>-\frac{1}{6}\left(-\frac{3}{5}\right)$$

Multiply -\frac{1}{6} times -\frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$x>\frac{-\left(-3\right)}{6\times 5}$$

Do the multiplications in the fraction \frac{-\left(-3\right)}{6\times 5}.

$$x>\frac{3}{30}$$

Reduce the fraction \frac{3}{30} to lowest terms by extracting and canceling out 3.

$$x>\frac{1}{10}$$