Solve.
|x-|1=3
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
• A. The solution set is
3. (Use a comma to separate answers as needed.)
• B. The solution is the empty set.
To solve the equation |x-|1|=3, we can start by simplifying the expression inside the outer absolute value.
|x-|1|=3
|x-1|=3
Now, we can set up two separate equations, one for when x-1 is positive and one for when x-1 is negative.
When x-1 is positive:
x-1 = 3
Solving for x, we add 1 to both sides:
x = 4
When x-1 is negative:
x-1 = -3
Solving for x, we add 1 to both sides:
x = -2
Therefore, the solution set is {4, -2}.
A. The solution set is 4, -2.