Solve -7(v+6)+24geq3(2-v)

$$- 7 ( v + 6 ) + 24 \geq 3 ( 2 - v )$$

Solve for v

$$v\leq -6$$

Solution Steps

Use the distributive property to multiply -7 by v+6.

$$-7v-42+24\geq 3\left(2-v\right)$$

Add -42 and 24 to get -18.

$$-7v-18\geq 3\left(2-v\right)$$

Use the distributive property to multiply 3 by 2-v.

$$-7v-18\geq 6-3v$$

Add 3v to both sides.

$$-7v-18+3v\geq 6$$

Combine -7v and 3v to get -4v.

$$-4v-18\geq 6$$

Add 18 to both sides.

$$-4v\geq 6+18$$

Add 6 and 18 to get 24.

$$-4v\geq 24$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$v\leq \frac{24}{-4}$$

Divide 24 by -4 to get -6.

$$v\leq -6$$