Solve 9/4-1/2k>5

$$\frac { 9 } { 4 } - \frac { 1 } { 2 } k > 5$$

Solve for k

$$k<-\frac{11}{2}$$

Solution Steps

Subtract \frac{9}{4} from both sides.

$$-\frac{1}{2}k>5-\frac{9}{4}$$

Convert 5 to fraction \frac{20}{4}.

$$-\frac{1}{2}k>\frac{20}{4}-\frac{9}{4}$$

Since \frac{20}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{2}k>\frac{20-9}{4}$$

Subtract 9 from 20 to get 11.

$$-\frac{1}{2}k>\frac{11}{4}$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}. Since -\frac{1}{2} is negative, the inequality direction is changed.

$$k<\frac{11}{4}\left(-2\right)$$

Express \frac{11}{4}\left(-2\right) as a single fraction.

$$k<\frac{11\left(-2\right)}{4}$$

Multiply 11 and -2 to get -22.

$$k<\frac{-22}{4}$$

Reduce the fraction \frac{-22}{4} to lowest terms by extracting and canceling out 2.

$$k<-\frac{11}{2}$$