Solve -3x-9geq1/9x-3

$$- 3 x - 9 \geq \frac { 1 } { 9 } x - 3$$

Solve for x

$$x\leq -\frac{27}{14}$$

Solution Steps

Subtract \frac{1}{9}x from both sides.

$$-3x-9-\frac{1}{9}x\geq -3$$

Combine -3x and -\frac{1}{9}x to get -\frac{28}{9}x.

$$-\frac{28}{9}x-9\geq -3$$

Add 9 to both sides.

$$-\frac{28}{9}x\geq -3+9$$

Add -3 and 9 to get 6.

$$-\frac{28}{9}x\geq 6$$

Multiply both sides by -\frac{9}{28}, the reciprocal of -\frac{28}{9}. Since -\frac{28}{9} is negative, the inequality direction is changed.

$$x\leq 6\left(-\frac{9}{28}\right)$$

Express 6\left(-\frac{9}{28}\right) as a single fraction.

$$x\leq \frac{6\left(-9\right)}{28}$$

Multiply 6 and -9 to get -54.

$$x\leq \frac{-54}{28}$$

Reduce the fraction \frac{-54}{28} to lowest terms by extracting and canceling out 2.

$$x\leq -\frac{27}{14}$$