Solve 16-2(9x-9)geq3x-8(3-x)

$$16 - 2 ( 9 x - 9 ) \geq 3 x - 8 ( 3 - x )$$

Solve for x

$$x\leq 2$$

Solution Steps

Use the distributive property to multiply -2 by 9x-9.

$$16-18x+18\geq 3x-8\left(3-x\right)$$

Add 16 and 18 to get 34.

$$34-18x\geq 3x-8\left(3-x\right)$$

Use the distributive property to multiply -8 by 3-x.

$$34-18x\geq 3x-24+8x$$

Combine 3x and 8x to get 11x.

$$34-18x\geq 11x-24$$

Subtract 11x from both sides.

$$34-18x-11x\geq -24$$

Combine -18x and -11x to get -29x.

$$34-29x\geq -24$$

Subtract 34 from both sides.

$$-29x\geq -24-34$$

Subtract 34 from -24 to get -58.

$$-29x\geq -58$$

Divide both sides by -29. Since -29 is negative, the inequality direction is changed.

$$x\leq \frac{-58}{-29}$$

Divide -58 by -29 to get 2.

$$x\leq 2$$