Question

solve the absolute value equation or indicate that the equation has no solution
3|2x - 3| = 21

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is
(simplify your answer use a comma to separate answers as needed )
b. the solution set is the empty set

Explanation:

Step1: Isolate absolute value term

Divide both sides by 3:
$$\frac{3|2x-3|}{3} = \frac{21}{3}$$
Simplify to get $|2x-3| = 7$

Step2: Split into two linear equations

Absolute value gives two cases:
$2x - 3 = 7$ or $2x - 3 = -7$

Step3: Solve first linear equation

Add 3 to both sides:
$2x = 7 + 3$
$2x = 10$
Divide by 2: $x = \frac{10}{2} = 5$

Step4: Solve second linear equation

Add 3 to both sides:
$2x = -7 + 3$
$2x = -4$
Divide by 2: $x = \frac{-4}{2} = -2$

Answer:

A. The solution set is {5, -2}