Solve the absolute value equation.
StartAbsoluteValue 10 x minus 3 EndAbsoluteValue minus 11 equals 2
Question content area bottom
Part 1
Select the correct choice below, and fill in the answer box if necessary.
A.
xequals
enter your response here
(Use a comma to separate answers as needed.)
B.
There are no solutions.
To solve the absolute value equation |10x - 3| - 11 = 2, we can start by isolating the absolute value term.
|10x - 3| = 2 + 11
|10x - 3| = 13
Now, we can break the equation into two separate cases:
Case 1: (10x - 3) = 13
Solving for x in this case, we have:
10x - 3 = 13
10x = 16
x = 16/10
x = 8/5
Case 2: -(10x - 3) = 13
Solving for x in this case, we have:
-10x + 3 = 13
-10x = 13 - 3
-10x = 10
x = 10/(-10)
x = -1
So the solutions to the absolute value equation are x = 8/5 and x = -1.
Therefore, the correct choice is:
A. x = 8/5, -1