Solve 2-1/2xleqx+3

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

Solve for x

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

Solution Steps

Subtract x from both sides.

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

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

$$2-\frac{3}{2}x\leq 3$$

Subtract 2 from both sides.

$$-\frac{3}{2}x\leq 3-2$$

Subtract 2 from 3 to get 1.

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

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}. Since -\frac{3}{2} is negative, the inequality direction is changed.

$$x\geq 1\left(-\frac{2}{3}\right)$$

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

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