Final answer:
An absolute value equation with solutions x=8 and x=18 is |x - 13| = 5, representing the distance of x being 5 units from the midpoint 13.
Step-by-step explanation:
To write an absolute value equation with the solutions of x=8 and x=18, you want the distance between x and the midpoint of the two solutions to be equal to half the distance between the two solutions. The midpoint of 8 and 18 is 13, and half the distance between them is 5. Thus, the absolute value equation that has 8 and 18 as solutions is |x - 13| = 5. This equation means that x is 5 units away from the midpoint, on either side, which gives us the two solutions when we solve the equation:
x - 13 = 5 which gives x = 18
x - 13 = -5 which gives x = 8