Solve -3(v+4)+34leq5(2-v)

$$- 3 ( v + 4 ) + 34 \leq 5 ( 2 - v )$$

Solve for v

$$v\leq -6$$

Solution Steps

Use the distributive property to multiply -3 by v+4.

$$-3v-12+34\leq 5\left(2-v\right)$$

Add -12 and 34 to get 22.

$$-3v+22\leq 5\left(2-v\right)$$

Use the distributive property to multiply 5 by 2-v.

$$-3v+22\leq 10-5v$$

Add 5v to both sides.

$$-3v+22+5v\leq 10$$

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

$$2v+22\leq 10$$

Subtract 22 from both sides.

$$2v\leq 10-22$$

Subtract 22 from 10 to get -12.

$$2v\leq -12$$

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

$$v\leq \frac{-12}{2}$$

Divide -12 by 2 to get -6.

$$v\leq -6$$