Solve 3-2v/5-3v+2/2>-8

$$\frac { 3 - 2 v } { 5 } - \frac { 3 v + 2 } { 2 } > - 8$$

Solve for v

$$v<4$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 5,2. Since 10 is positive, the inequality direction remains the same.

$$2\left(3-2v\right)-5\left(3v+2\right)>-80$$

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

$$6-4v-5\left(3v+2\right)>-80$$

Use the distributive property to multiply -5 by 3v+2.

$$6-4v-15v-10>-80$$

Combine -4v and -15v to get -19v.

$$6-19v-10>-80$$

Subtract 10 from 6 to get -4.

$$-4-19v>-80$$

Add 4 to both sides.

$$-19v>-80+4$$

Add -80 and 4 to get -76.

$$-19v>-76$$

Divide both sides by -19. Since -19 is negative, the inequality direction is changed.

$$v<\frac{-76}{-19}$$

Divide -76 by -19 to get 4.

$$v<4$$