Solve 2/3(5-x)geq6

$$\frac { 2 } { 3 } ( 5 - x ) \geq 6$$

Solve for x

$$x\leq -4$$

Solution Steps

Multiply both sides by \frac{3}{2}, the reciprocal of \frac{2}{3}. Since \frac{2}{3} is positive, the inequality direction remains the same.

$$5-x\geq 6\times \frac{3}{2}$$

Express 6\times \frac{3}{2} as a single fraction.

$$5-x\geq \frac{6\times 3}{2}$$

Multiply 6 and 3 to get 18.

$$5-x\geq \frac{18}{2}$$

Divide 18 by 2 to get 9.

$$5-x\geq 9$$

Subtract 5 from both sides.

$$-x\geq 9-5$$

Subtract 5 from 9 to get 4.

$$-x\geq 4$$

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

$$x\leq -4$$