Question

Consider the compound inequality x < 4 and x>a. If a=4 and the compounding word were "or" instead of "and",what would the solution be?Explain your answer

Answer 1

Answer:

We have:

x < 4 AND x > a.

if a = 4 and we use an "or" instead of the "and" we have:

x < 4 or x > 4.

This is:

"x is larger than 4 or smaller than 4."

Then the solution of this is all the real numbers except the value x = 4.

The set of solutions can be written as:

{xI x ∈ R  \ [4]}

Where this reads:

"x belongs to the set of the reals minus the number 4".

Or we also could write it as:

x ∈ (-∞, 4) ∪ (4, ∞)

Where we have two open ends in the "4" side, so the value x = 4 does not belong to that set.