Question

What is the solution set for the inequality x < -2 or x > 6

Answer 1

he solution set is

{ x ∣ x > 1 } .

Explanation

For each of these inequalities, there will be a set of

x

-values that make them true. For example, it's pretty clear that large values of

x

(like 1,000) work for both, and negative values (like -1,000) will not work for either.

Since we're asked to solve a "this OR that" pair of inequalities, what we'd like to know are all the

x

-values that will work for at least one of them. To do this, we solve both inequalities for

x

, and then overlap the two solution set