Solve 13-3(x-6)leq3x+7

$$13 - 3 ( x - 6 ) \leq 3 x + 7$$

Solve for x

$$x\geq 4$$

Solution Steps

Use the distributive property to multiply -3 by x-6.

$$13-3x+18\leq 3x+7$$

Add 13 and 18 to get 31.

$$31-3x\leq 3x+7$$

Subtract 3x from both sides.

$$31-3x-3x\leq 7$$

Combine -3x and -3x to get -6x.

$$31-6x\leq 7$$

Subtract 31 from both sides.

$$-6x\leq 7-31$$

Subtract 31 from 7 to get -24.

$$-6x\leq -24$$

Divide both sides by -6. Since -6 is negative, the inequality direction is changed.

$$x\geq \frac{-24}{-6}$$

Divide -24 by -6 to get 4.

$$x\geq 4$$