Solve 7/4-3x<5/6

$$\frac { 7 } { 4 } - 3 x < \frac { 5 } { 6 }$$

Solve for x

$$x>\frac{11}{36}$$

Solution Steps

Subtract \frac{7}{4} from both sides.

$$-3x<\frac{5}{6}-\frac{7}{4}$$

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{7}{4} to fractions with denominator 12.

$$-3x<\frac{10}{12}-\frac{21}{12}$$

Since \frac{10}{12} and \frac{21}{12} have the same denominator, subtract them by subtracting their numerators.

$$-3x<\frac{10-21}{12}$$

Subtract 21 from 10 to get -11.

$$-3x<-\frac{11}{12}$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x>\frac{-\frac{11}{12}}{-3}$$

Express \frac{-\frac{11}{12}}{-3} as a single fraction.

$$x>\frac{-11}{12\left(-3\right)}$$

Multiply 12 and -3 to get -36.

$$x>\frac{-11}{-36}$$

Fraction \frac{-11}{-36} can be simplified to \frac{11}{36} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{11}{36}$$