Question

What kind of compound inequality is

4x-5≥3
Or
5-x > 8
?
a. hole
b. intersection
c. conjunction
d. union

Answer 1

Answer: D) union

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Step-by-step explanation:

Let's solve the first inequality for x.

4x-5 ≥ 3

4x ≥ 3+5

4x ≥ 8

x ≥ 8/4

x ≥ 2

Now solve the other inequality

5 - x > 8

5 > 8+x

8+x < 5

x < 5-8

x < -3

The two solutions we get are x < -3 or x ≥ 2

These two regions do not overlap. The key word "or" connecting the original inequalities also applies to the solutions.

Either x is smaller than -3, OR it is 2 or larger

I recommend drawing out a number line and shading the appropriate regions. The two disjoint regions do not connect which means we have a union of the two regions.