Question

solve the absolute value equation or indicate that the equation has no solution.
3|2x - 5| = 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: Divide both sides by 3

To isolate the absolute value expression, we divide both sides of the equation \( 3|2x - 5| = 21 \) by 3.
\( \frac{3|2x - 5|}{3}=\frac{21}{3} \)
Simplifying, we get \( |2x - 5| = 7 \)

Step2: Set up two equations

The absolute value equation \( |2x - 5| = 7 \) means that \( 2x - 5 = 7 \) or \( 2x - 5 = -7 \)

For \( 2x - 5 = 7 \):

Step3: Solve for x

Add 5 to both sides: \( 2x - 5 + 5 = 7 + 5 \)
Simplify: \( 2x = 12 \)
Divide both sides by 2: \( \frac{2x}{2}=\frac{12}{2} \)
So, \( x = 6 \)

For \( 2x - 5 = -7 \):

Step4: Solve for x

Add 5 to both sides: \( 2x - 5 + 5 = -7 + 5 \)
Simplify: \( 2x = -2 \)
Divide both sides by 2: \( \frac{2x}{2}=\frac{-2}{2} \)
So, \( x = -1 \)

Answer:

A. The solution set is \( \{ -1, 6 \} \)