Question

solve the absolute value equation or indicate that the equation has no solution. 5|2x - 1| = 25 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 the absolute - value expression

Divide both sides of the equation $5|2x - 1|=25$ by 5.
$|2x - 1|=\frac{25}{5}=5$

Step2: Set up two equations

Since $|a| = b$ ($b\geq0$) is equivalent to $a = b$ or $a=-b$, we set up two equations:
$2x - 1 = 5$ or $2x - 1=-5$

Step3: Solve the first equation

For $2x - 1 = 5$, add 1 to both sides: $2x=5 + 1=6$. Then divide both sides by 2: $x=\frac{6}{2}=3$.

Step4: Solve the second equation

For $2x - 1=-5$, add 1 to both sides: $2x=-5 + 1=-4$. Then divide both sides by 2: $x=\frac{-4}{2}=-2$.

Answer:

A. The solution set is $\{-2,3\}$