Answer:
(d) -2x -8 < -44 and -2x -8 ≥ -8
Explanation:
A compound inequality is a mathematical sentence that combines two simple inequalities. A solution will satisfy both inequalities. That is, it represents an "and" (intersection) condition for the solution sets.
Equivalent pair
An inequality of the form ...
a > b ≥ c
can be written as a pair of inequalities by considering what is on either side of each of the relation symbols:
- left symbol: a > b
- right symbol: b ≥ c
Application
Given: -44 > -2x -8 ≥ -8
We can decompose the given inequality into the system ...
- -44 > -2x -8 . . . . . . . . left symbol
- -2x -8 ≥ -8 . . . . . . . . . right symbol
When we compare these to the offered answer choices, we see that we need to rewrite the first inequality so the constant is on the right:
-2x -8 < -44
Then the equivalent form of the given inequality is ...
-2x -8 < -44 and -2x -8 ≥ -8
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Additional comment
The transitive property of inequality means that ...
a > b ≥ c
implies that a > c.
You will notice that our given inequality, written in this way, becomes ...
-44 > -8 . . . . . . not true
This means the inequality has no solution. (The solution set is the empty set.)