Solve |2v+1|-3/4=1/2-|2v+1|

$$\frac { | 2 v + 1 | - 3 } { 4 } = \frac { 1 } { 2 } - | 2 v + 1 |$$

Solve for v

$$v=-1$$

$$v=0$$

Steps Using Definition of Absolute Value

Multiply both sides of the equation by 4, the least common multiple of 4,2.

$$|2v+1|-3=2-4|2v+1|$$

Add 4|2v+1| to both sides.

$$|2v+1|-3+4|2v+1|=2$$

Combine |2v+1| and 4|2v+1| to get 5|2v+1|.

$$5|2v+1|-3=2$$

Add 3 to both sides.

$$5|2v+1|=2+3$$

Add 2 and 3 to get 5.

$$5|2v+1|=5$$

Divide both sides by 5.

$$|2v+1|=\frac{5}{5}$$

Divide 5 by 5 to get 1.

$$|2v+1|=1$$

Use the definition of absolute value.

$$2v+1=1 2v+1=-1$$

Subtract 1 from both sides of the equation.

$$2v=0 2v=-2$$

Divide both sides by 2.

$$v=0 v=-1$$