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Which of the following is an equivalent form of the compound inequality -44 > -2x - 82-8?
0-2x - 8 >-44 and -2x - 82-8
O-2x > -44 and -8-8
0-2x - 8<-44 and -2x -85-8
0-2x -8<-44 and -2x - 82-8


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sqdancefan

Answer:

  (d)  -2x -8 < -44  and -2x -8 ≥ -8

Step-by-step 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.)

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