Explanation:
To find an absolute value equation with the solution set {-2 1/2, 3 1/2}, we can use the fact that the absolute value of a number can be positive or negative, depending on whether the number is greater than or less than zero.
For the first solution, -2 1/2, the equation can be written as:
|x + 2 1/2| = -(-2 1/2)
Since the absolute value of any number is always non-negative, the equation with a negative value on the right-hand side will not have a solution. Therefore, there is no absolute value equation that has -2 1/2 as a solution.
For the second solution, 3 1/2, the equation can be written as:
|x - 3 1/2| = 3 1/2
This equation states that the distance between x and 3 1/2 is equal to 3 1/2. This will have two possible solutions, one where x is 3 1/2 units to the right of 3 1/2 (giving x = 7) and another where x is 3 1/2 units to the left of 3 1/2 (giving x = 0).
Therefore, the absolute value equation with the solution set {-2 1/2, 3 1/2} is:
|x - 3 1/2| = 3 1/2
which has solutions x = 0 and x = 7.