Question

Solve the compound inequality for x and identify the graph of its solution. x + 7 < 3 or x - 52 -1 O A. Solution: x < -4 or X2 4 -5 -4 -3 -2 -1 0 0 1 6 4 5 B. Solution: x-4 and x 4 -5 -4 -3 -2 -1 -3 -2 -1 0 1 2 6 4 5 C. Solution: xs-4 or x>4 00 -5 -4 -3 -2 -1 0 1 2 6 D. Solution. x < -4 or x > 4 -5 -4 -3 -2 -1 0 1 2 3 4 5​

Answer 1

D. x < -4 or x ≥ 4

Explanation:

You can eliminate choices A and B because the graph and the inequalities do not agree.

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You can eliminate choice C because the first inequality tells you ...

x < some value

That means the shading will be to the left of an open circle.

This is only shown in Choice D.

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Additional comment

You can work multiple choice questions several different ways. I like to choose the simplest, which often means you do not actually need to work the problem. You only need to be able to identify ...

• answers that are self-consistent
• answers that are consistent with problem requirements
• answers that are consistent with numerical and geometric facts

Here, we can eliminate incorrect answers by throwing out those that are not self-consistent and that are not consistent with the problem statement.

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If we were to solve the inequalities, we would subtract 7 from both sides of the first one:

x +7 < 3

x < -4 . . . . . . subtract 7 from both sides

and we would add 5 to both sides of the second one:

x -5 ≥ -1

x ≥ 4 . . . . . . add 5 to both sides

If you write these inequalities so the symbols point left, you have ...

x < -4 or 4 ≤ x

This tells you shading is "outside" the segment between -4 and 4, and that there is an open-circle at x=-4. This is consistent with the number lines of choices B and D. However, these inequalities are not consistent with what is written in choice B.