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

$$1 / 2 x + 2 \geq 1 / 3 x - 4$$

Solve for x

$$x\geq -36$$

Solution Steps

Subtract \frac{1}{3}x from both sides.

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

Combine \frac{1}{2}x and -\frac{1}{3}x to get \frac{1}{6}x.

$$\frac{1}{6}x+2\geq -4$$

Subtract 2 from both sides.

$$\frac{1}{6}x\geq -4-2$$

Subtract 2 from -4 to get -6.

$$\frac{1}{6}x\geq -6$$

Multiply both sides by 6, the reciprocal of \frac{1}{6}. Since \frac{1}{6} is positive, the inequality direction remains the same.

$$x\geq -6\times 6$$

Multiply -6 and 6 to get -36.

$$x\geq -36$$