Solve 3/2-kgeqk+1/2

$$\frac { 3 } { 2 } - k \geq k + \frac { 1 } { 2 }$$

Solve for k

$$k\leq \frac{1}{2}$$

Solution Steps

Subtract k from both sides.

$$\frac{3}{2}-k-k\geq \frac{1}{2}$$

Combine -k and -k to get -2k.

$$\frac{3}{2}-2k\geq \frac{1}{2}$$

Subtract \frac{3}{2} from both sides.

$$-2k\geq \frac{1}{2}-\frac{3}{2}$$

Since \frac{1}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$-2k\geq \frac{1-3}{2}$$

Subtract 3 from 1 to get -2.

$$-2k\geq \frac{-2}{2}$$

Divide -2 by 2 to get -1.

$$-2k\geq -1$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$k\leq \frac{-1}{-2}$$

Fraction \frac{-1}{-2} can be simplified to \frac{1}{2} by removing the negative sign from both the numerator and the denominator.

$$k\leq \frac{1}{2}$$