Here, the union tells us that at least one of the original inequalities must be true. We solve each separately, first.
x + 2 < 5 OR x - 7 > -6
x < 3 OR x - 7 > -6 subtract 2 on both sides of the equation left of the OR
x < 3 OR x > 1 add 7 on both sides of the equation right of the OR
Thus x < 3 or x > 1. In set notation, {x | x < 3 or x > 1} is true.
