Solve -3(w+6)+24>5(4-w)

$$- 3 ( w + 6 ) + 24 > 5 ( 4 - w )$$

Solve for w

$$w>7$$

Solution Steps

Use the distributive property to multiply -3 by w+6.

$$-3w-18+24>5\left(4-w\right)$$

Add -18 and 24 to get 6.

$$-3w+6>5\left(4-w\right)$$

Use the distributive property to multiply 5 by 4-w.

$$-3w+6>20-5w$$

Add 5w to both sides.

$$-3w+6+5w>20$$

Combine -3w and 5w to get 2w.

$$2w+6>20$$

Subtract 6 from both sides.

$$2w>20-6$$

Subtract 6 from 20 to get 14.

$$2w>14$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$w>\frac{14}{2}$$

Divide 14 by 2 to get 7.

$$w>7$$