Final answer:
The absolute value equation with the solutions x=-10 and x=-5 is |x + 7.5| = 5.
Step-by-step explanation:
To write an absolute value equation with the solutions x=-10 and x=-5, you must recognize that the absolute value expression will equal to 5, because the distance from each of these points to the axis of symmetry (which in this case is the point exactly between x=-10 and x=-5, which is x=-7.5) is 5. Therefore, the equation is |x + 7.5| = 5. This equation will have x=-10 and x=-5 as solutions because both of these x values are 5 units away from -7.5 on the number line.