Question

Solve (x + 2 < 5) U (x - 7 > -6).

Answer 1

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.