Solve -1/2x-2geq1/2x+3/4

$$- \frac { 1 } { 2 } x - 2 \geq \frac { 1 } { 2 } x + \frac { 3 } { 4 }$$

Solve for x

$$x\leq -\frac{11}{4}$$

Solution Steps

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

$$-\frac{1}{2}x-2-\frac{1}{2}x\geq \frac{3}{4}$$

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

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

Add 2 to both sides.

$$-x\geq \frac{3}{4}+2$$

Convert 2 to fraction \frac{8}{4}.

$$-x\geq \frac{3}{4}+\frac{8}{4}$$

Since \frac{3}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$-x\geq \frac{3+8}{4}$$

Add 3 and 8 to get 11.

$$-x\geq \frac{11}{4}$$

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

$$x\leq \frac{\frac{11}{4}}{-1}$$

Express \frac{\frac{11}{4}}{-1} as a single fraction.

$$x\leq \frac{11}{4\left(-1\right)}$$

Multiply 4 and -1 to get -4.

$$x\leq \frac{11}{-4}$$

Fraction \frac{11}{-4} can be rewritten as -\frac{11}{4} by extracting the negative sign.

$$x\leq -\frac{11}{4}$$