Answers:
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Explanation:
For each inequality given, we need to isolate x. We'll solve for x in pretty much the same way we solve an equation. So if we wanted to solve 2x = 12, we would divide both sides by 2 to get x = 6.
Similarly, solving 2x > 12 would lead to x > 6. The inequality sign does not flip. It only flips if you divide both sides by a negative number.
The graph of x > 6 has an open hole at 6 and shading to the right. So that matches with graph D.
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Solving 7x < 42 leads to x < 6 when we divide both sides by 7. The graph has the open hole at the same endpoint of 6, but now the shading is to the left. This shows all values smaller than 6. Therefore 7x < 42 matches with graph A.
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We have 3x > 15 match with graph C because that inequality is the same as x > 5, after we divide both sides by 3. We have an open hole at 5 and shading to the right.
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Lastly, the inequality x+1 < 8 solves to x < 7. We'll have an open hole at 7 and shading to the left. This describes graph B.
Any time you see an open hole, it means "do not include this value as part of the solution set". For instance, with x < 7, we have x = 7 as the open hole. This is because 7 < 7 is a false statement. A number cannot be smaller than itself.