Solve 3-8+2x+15leq9x-23+2x+12

$$3 - 8 + 2 x + 15 \leq 9 x - 23 + 2 x + 12$$

Solve for x

$$x\geq \frac{7}{3}$$

Solution Steps

Subtract 8 from 3 to get -5.

$$-5+2x+15\leq 9x-23+2x+12$$

Add -5 and 15 to get 10.

$$10+2x\leq 9x-23+2x+12$$

Combine 9x and 2x to get 11x.

$$10+2x\leq 11x-23+12$$

Add -23 and 12 to get -11.

$$10+2x\leq 11x-11$$

Subtract 11x from both sides.

$$10+2x-11x\leq -11$$

Combine 2x and -11x to get -9x.

$$10-9x\leq -11$$

Subtract 10 from both sides.

$$-9x\leq -11-10$$

Subtract 10 from -11 to get -21.

$$-9x\leq -21$$

Divide both sides by -9. Since -9 is negative, the inequality direction is changed.

$$x\geq \frac{-21}{-9}$$

Reduce the fraction \frac{-21}{-9} to lowest terms by extracting and canceling out -3.

$$x\geq \frac{7}{3}$$