Solve 5/6*-2/5>3/4x-1/10

$$\frac { 5 } { 6 } \times - \frac { 2 } { 5 } > \frac { 3 } { 4 } x - \frac { 1 } { 10 }$$

Solve for x

$$x<-\frac{14}{45}$$

Solution Steps

Multiply \frac{5}{6} times -\frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-2\right)}{6\times 5}>\frac{3}{4}x-\frac{1}{10}$$

Cancel out 5 in both numerator and denominator.

$$\frac{-2}{6}>\frac{3}{4}x-\frac{1}{10}$$

Reduce the fraction \frac{-2}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{3}>\frac{3}{4}x-\frac{1}{10}$$

Swap sides so that all variable terms are on the left hand side. This changes the sign direction.

$$\frac{3}{4}x-\frac{1}{10}<-\frac{1}{3}$$

Add \frac{1}{10} to both sides.

$$\frac{3}{4}x<-\frac{1}{3}+\frac{1}{10}$$

Least common multiple of 3 and 10 is 30. Convert -\frac{1}{3} and \frac{1}{10} to fractions with denominator 30.

$$\frac{3}{4}x<-\frac{10}{30}+\frac{3}{30}$$

Since -\frac{10}{30} and \frac{3}{30} have the same denominator, add them by adding their numerators.

$$\frac{3}{4}x<\frac{-10+3}{30}$$

Add -10 and 3 to get -7.

$$\frac{3}{4}x<-\frac{7}{30}$$

Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}. Since \frac{3}{4} is positive, the inequality direction remains the same.

$$x<-\frac{7}{30}\times \frac{4}{3}$$

Multiply -\frac{7}{30} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$x<\frac{-7\times 4}{30\times 3}$$

Do the multiplications in the fraction \frac{-7\times 4}{30\times 3}.

$$x<\frac{-28}{90}$$

Reduce the fraction \frac{-28}{90} to lowest terms by extracting and canceling out 2.

$$x<-\frac{14}{45}$$