Answer:
D. x < -4 or x ≥ 4
Step-by-step 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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<em>Additional comment</em>
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 <em>not consistent</em> with what is written in choice B.
