Solve 1/2-1/3xgeq3/2+2/3x

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

Solve for x

$$x\leq -1$$

Solution Steps

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

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

Combine -\frac{1}{3}x and -\frac{2}{3}x to get -x.

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

Subtract \frac{1}{2} from both sides.

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

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

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

Subtract 1 from 3 to get 2.

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

Divide 2 by 2 to get 1.

$$-x\geq 1$$

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

$$x\leq -1$$