Answer:
<em>An equivalent form of the compound inequality </em>is the pair of single inequalities:
- -2x - 8 < - 44, and
- −2x − 8 ≥ −8
Explanation:
You can split the compound inequality into two equivalent inequalities by taking each side from the variable.
The compound inequality −44 > −2x − 8 ≥ −8 means that two conditions must be satisfied:
1. From the left side: - 44 > - 2x - 8
2. From the right side: −2x − 8 ≥ −8
Then, as a first approach you can tell that an equivalent form of the compound inequality is the pair of single inequalities:
- -44 > -2x - 8, and
- −2x − 8 ≥ −8
You should put the variable on the left sides, which will yield the best form of an equivalent pair of inequalitis.
- - 2x - 8 < -44, and
- - 2x - 8 ≥ - 8
That is the best choice of an equivalent form, and from there you can solve the inequalities which will permit to obtain the solution. Of course, you can manipulate the variable and find many other equivalent forms.
Notice, that both inequalities must be satisfied simultaneously.
This is how you solve that system
Add 8 to both sides: - 2x < -36
Divide both sides by - 2 (you have to change the sign): x > 18
-
Add 8 to both sides: - 2x ≥ 0
Divide by - 2 (again, you must change the sign): x ≤ 0
Then, the solution set is:
- x > 18 and x ≤ 0 and that is an empty set, since x cannot be at the same time greater than 18 and less or equal to 0.
This is, you conclude that the compound inequality is false, because there is not a value of x which is a solution.
