Solve the absolute value equation.
|2x-1| =3
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution set is }
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
• B. The solution set is no solution.
To solve the absolute value equation, we can set up two separate equations without the absolute value sign.
When the expression inside the absolute value is positive:
2x-1 = 3
Adding 1 to both sides:
2x = 4
Dividing both sides by 2:
x = 2
When the expression inside the absolute value is negative:
-(2x-1) = 3
Multiplying both sides by -1:
2x-1 = -3
Adding 1 to both sides:
2x = -2
Dividing both sides by 2:
x = -1
Therefore, the solution set is {-1, 2}. Answer: A