Solve -2x-5+x+3geq1/2x

$$- 2 x - 5 + x + 3 \geq \frac { 1 } { 2 } x$$

Solve for x

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

Solution Steps

Combine -2x and x to get -x.

$$-x-5+3\geq \frac{1}{2}x$$

Add -5 and 3 to get -2.

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

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

$$-x-2-\frac{1}{2}x\geq 0$$

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

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

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

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

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

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

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

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

Multiply 2 and -2 to get -4.

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

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

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