Solve {l}{xgeq6000}{-1/2x}

$$\left. \begin{array} { l } { x \geq 6000 } \\ { - \frac { 1 } { 2 } x } \end{array} \right.$$

Solve for x

$$x\geq 4000$$

Solution Steps

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

$$x+\frac{1}{2}x\geq 6000$$

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

$$\frac{3}{2}x\geq 6000$$

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

$$x\geq 6000\times \frac{2}{3}$$

Express 6000\times \frac{2}{3} as a single fraction.

$$x\geq \frac{6000\times 2}{3}$$

Multiply 6000 and 2 to get 12000.

$$x\geq \frac{12000}{3}$$

Divide 12000 by 3 to get 4000.

$$x\geq 4000$$