Solve -2/3x-2leq2/3x

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

Solve for x

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

Solution Steps

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

$$-\frac{2}{3}x-2-\frac{2}{3}x\leq 0$$

Combine -\frac{2}{3}x and -\frac{2}{3}x to get -\frac{4}{3}x.

$$-\frac{4}{3}x-2\leq 0$$

Add 2 to both sides. Anything plus zero gives itself.

$$-\frac{4}{3}x\leq 2$$

Multiply both sides by -\frac{3}{4}, the reciprocal of -\frac{4}{3}. Since -\frac{4}{3} is negative, the inequality direction is changed.

$$x\geq 2\left(-\frac{3}{4}\right)$$

Express 2\left(-\frac{3}{4}\right) as a single fraction.

$$x\geq \frac{2\left(-3\right)}{4}$$

Multiply 2 and -3 to get -6.

$$x\geq \frac{-6}{4}$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

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