Solve 3/4(1/2-x/8)geq3

$$\frac { 3 } { 4 } ( \frac { 1 } { 2 } - \frac { x } { 8 } ) \geq 3$$

Solve for x

$$x\leq -28$$

Solution Steps

Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}. Since \frac{3}{4} is positive, the inequality direction remains the same.

$$\frac{1}{2}-\frac{x}{8}\geq 3\times \frac{4}{3}$$

Cancel out 3 and 3.

$$\frac{1}{2}-\frac{x}{8}\geq 4$$

Multiply both sides of the equation by 8, the least common multiple of 2,8. Since 8 is positive, the inequality direction remains the same.

$$4-x\geq 32$$

Subtract 4 from both sides.

$$-x\geq 32-4$$

Subtract 4 from 32 to get 28.

$$-x\geq 28$$

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

$$x\leq -28$$