Question

Suppose that a < b. Select from the symbols >,< as well as words and and or, to complete the compound inequality below so that it’s solution is all real numbers.

Answer 1

x > a or x < b

Explanation:

You want a compound inequality involving 'a' and 'b' with a < b, such that the solution set is all real numbers.

Overlap

The solution set will be all real numbers only if 'a' is included in the solution set of the inequality involving 'b', and vice versa. The conjunction must be "or" so the solution set of one inequality includes the complement of the other inequality's solution set.

Inequalities

For a < b, the inequalities that will satisfy the requirement above are ...

• x < b
• a < x . . . . also written as x > a

With the conjunction 'or', the desired compound inequality is ...

x > a or x < b