Question

solve the equation.\\
|2x - 3| = 6\\
select the correct choice below and, if necessary, fill in the answer box to complete your choice.\\
a. the solution set is \boxed{}.\\
(simplify your answer. type an integer or a fraction. use a comma to separate answers as needed.)\\
b. the solution is all real numbers.\\
c. the solution is the empty set.

Explanation:

Step1: Apply absolute value definition

The absolute value equation \(|2x - 3| = 6\) means \(2x - 3 = 6\) or \(2x - 3 = -6\).

Step2: Solve \(2x - 3 = 6\)

Add 3 to both sides: \(2x = 6 + 3 = 9\).
Divide by 2: \(x=\frac{9}{2}\).

Step3: Solve \(2x - 3 = -6\)

Add 3 to both sides: \(2x = -6 + 3 = -3\).
Divide by 2: \(x = -\frac{3}{2}\).

Answer:

\(\frac{9}{2}, -\frac{3}{2}\)