The absolute equation is .

Rewrite for Case 1 and Case 2.

Case 1: is nonnegative.

Apply addition property of equality: If then .

Add 3 to each side.

.

Apply division property of equality: If then .

Divide each side by 2.

Cancel common terms.

.

Case 2: is negative.

Product of two opposite signs is negative and product of two same signs is positive.

Apply subtraction property of equality: If then .

Subtract 3 from each side.

.

Apply division property of equality: If then .

Divide each side by negative 2.

Cancel common terms.

.

Therefore solution set is .

The option B is correct answer.