Solve 11(m+2)leq2m-(3m+8)

$$11 ( m + 2 ) \leq 2 m - ( 3 m + 8 )$$

Solve for m

$$m\leq -\frac{5}{2}$$

Solution Steps

Use the distributive property to multiply 11 by m+2.

$$11m+22\leq 2m-\left(3m+8\right)$$

To find the opposite of 3m+8, find the opposite of each term.

$$11m+22\leq 2m-3m-8$$

Combine 2m and -3m to get -m.

$$11m+22\leq -m-8$$

Add m to both sides.

$$11m+22+m\leq -8$$

Combine 11m and m to get 12m.

$$12m+22\leq -8$$

Subtract 22 from both sides.

$$12m\leq -8-22$$

Subtract 22 from -8 to get -30.

$$12m\leq -30$$

Divide both sides by 12. Since 12 is positive, the inequality direction remains the same.

$$m\leq \frac{-30}{12}$$

Reduce the fraction \frac{-30}{12} to lowest terms by extracting and canceling out 6.

$$m\leq -\frac{5}{2}$$