Solve 25-(x-5/6)>3/4

$$25 - ( x - \frac { 5 } { 6 } ) > \frac { 3 } { 4 }$$

Solve for x

$$x<\frac{301}{12}$$

Solution Steps

To find the opposite of x-\frac{5}{6}, find the opposite of each term.

$$25-x-\left(-\frac{5}{6}\right)>\frac{3}{4}$$

The opposite of -\frac{5}{6} is \frac{5}{6}.

$$25-x+\frac{5}{6}>\frac{3}{4}$$

Convert 25 to fraction \frac{150}{6}.

$$\frac{150}{6}-x+\frac{5}{6}>\frac{3}{4}$$

Since \frac{150}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$\frac{150+5}{6}-x>\frac{3}{4}$$

Add 150 and 5 to get 155.

$$\frac{155}{6}-x>\frac{3}{4}$$

Subtract \frac{155}{6} from both sides.

$$-x>\frac{3}{4}-\frac{155}{6}$$

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{155}{6} to fractions with denominator 12.

$$-x>\frac{9}{12}-\frac{310}{12}$$

Since \frac{9}{12} and \frac{310}{12} have the same denominator, subtract them by subtracting their numerators.

$$-x>\frac{9-310}{12}$$

Subtract 310 from 9 to get -301.

$$-x>-\frac{301}{12}$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x<\frac{-\frac{301}{12}}{-1}$$

Express \frac{-\frac{301}{12}}{-1} as a single fraction.

$$x<\frac{-301}{12\left(-1\right)}$$

Multiply 12 and -1 to get -12.

$$x<\frac{-301}{-12}$$

Fraction \frac{-301}{-12} can be simplified to \frac{301}{12} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{301}{12}$$