Solve 2x+13geq1/3x-7

$$2 x + 13 \geq 1 / 3 x - 7$$

Solve for x

$$x\geq -12$$

Solution Steps

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

$$2x+13-\frac{1}{3}x\geq -7$$

Combine 2x and -\frac{1}{3}x to get \frac{5}{3}x.

$$\frac{5}{3}x+13\geq -7$$

Subtract 13 from both sides.

$$\frac{5}{3}x\geq -7-13$$

Subtract 13 from -7 to get -20.

$$\frac{5}{3}x\geq -20$$

Multiply both sides by \frac{3}{5}, the reciprocal of \frac{5}{3}. Since \frac{5}{3} is positive, the inequality direction remains the same.

$$x\geq -20\times \frac{3}{5}$$

Express -20\times \frac{3}{5} as a single fraction.

$$x\geq \frac{-20\times 3}{5}$$

Multiply -20 and 3 to get -60.

$$x\geq \frac{-60}{5}$$

Divide -60 by 5 to get -12.

$$x\geq -12$$