Step 1 To solve |x-5|<2, first remove the absolute value. The inequality of the form |x| Step 2 To solve the inequality -2<x-5<2, add 5 to all the parts of the inequality and simplify as follows: -2<x-5<2 -2+5<x-5+5<2+5 3<x<7 Therefore, the solution of the inequality is (3, 7).