Solve 2x+3geq-1/2x

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

Solve for x

$$x\geq -\frac{6}{5}$$

Solution Steps

Add \frac{1}{2}x to both sides.

$$2x+3+\frac{1}{2}x\geq 0$$

Combine 2x and \frac{1}{2}x to get \frac{5}{2}x.

$$\frac{5}{2}x+3\geq 0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

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

Multiply both sides by \frac{2}{5}, the reciprocal of \frac{5}{2}. Since \frac{5}{2} is positive, the inequality direction remains the same.

$$x\geq -3\times \frac{2}{5}$$

Express -3\times \frac{2}{5} as a single fraction.

$$x\geq \frac{-3\times 2}{5}$$

Multiply -3 and 2 to get -6.

$$x\geq \frac{-6}{5}$$

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

$$x\geq -\frac{6}{5}$$