Answer
$$x=-28\quad \mathrm{or}\quad \:x=52$$
Work Step by Step
Since the value inside the absolute value can be positive or negative and get the same number, we must consider both options. Doing this, we find:
$$0.25x-3=-10\quad \mathrm{or}\quad \:0.25x-3=10 \\ x=-28\quad \mathrm{or}\quad \:x=52$$