Solve -3x-2/6x+7-21leq-3x+7

$$- 3 x - 2 / 6 x + 7 - 21 \leq - 3 x + 7$$

Solve for x

$$x\geq -63$$

Solution Steps

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$-3x-\frac{1}{3}x+7-21\leq -3x+7$$

Combine -3x and -\frac{1}{3}x to get -\frac{10}{3}x.

$$-\frac{10}{3}x+7-21\leq -3x+7$$

Subtract 21 from 7 to get -14.

$$-\frac{10}{3}x-14\leq -3x+7$$

Add 3x to both sides.

$$-\frac{10}{3}x-14+3x\leq 7$$

Combine -\frac{10}{3}x and 3x to get -\frac{1}{3}x.

$$-\frac{1}{3}x-14\leq 7$$

Add 14 to both sides.

$$-\frac{1}{3}x\leq 7+14$$

Add 7 and 14 to get 21.

$$-\frac{1}{3}x\leq 21$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}. Since -\frac{1}{3} is negative, the inequality direction is changed.

$$x\geq 21\left(-3\right)$$

Multiply 21 and -3 to get -63.

$$x\geq -63$$