Solve 4(v+1)-7=3(v-1)-v

$$4 ( v + 1 ) - 7 = 3 ( v - 1 ) - v$$

Solve for v

$$v=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by v+1.

$$4v+4-7=3\left(v-1\right)-v$$

Subtract 7 from 4 to get -3.

$$4v-3=3\left(v-1\right)-v$$

Use the distributive property to multiply 3 by v-1.

$$4v-3=3v-3-v$$

Combine 3v and -v to get 2v.

$$4v-3=2v-3$$

Subtract 2v from both sides.

$$4v-3-2v=-3$$

Combine 4v and -2v to get 2v.

$$2v-3=-3$$

Add 3 to both sides.

$$2v=-3+3$$

Add -3 and 3 to get 0.

$$2v=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 2 is not equal to 0, v must be equal to 0.

$$v=0$$