Question

Identify the Intequality that corresponds to the graph below. Choose all that apply.

x <5
x-7≤ -2
x>5
x-7>-2

Answer 1

The answer would be the last two options, x > 5 and x-7>-2

Step-by-step explanation:
Since the arrow is pointing to the right and the circle isn't colored in we can assume that the sign should be >, this eliminates the first 2 options.

Now we can see that the arrow is pointing right from 5, so the third option is true.

For the last option, more steps are required.
x - 7 > -2
You need to isolate x, in order to do this add 7 to both sides
-2 + 7 = 5 ( It's like 7 - 2 )
So your equation should now be
x > 5

Now you can see that the last two options are true.

Answer 2

Answers are choice C and choice D

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Explanations:

Let's go through the answers one by one. We'll either confirm the answer or cross it off the list.

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Choice A: x < 5

This is not an answer because the shaded region is to the right of the value 5. If it were x > 5, then it would work. Cross this off the list.

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Choice B: x-7 <= -2

Add 7 to both sides and we'll get x <= 5. The same issue comes up as it did with choice A. This describes values smaller than 5 or equal to 5. Cross this off the list.

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Choice C: x > 5

This is one of the answers. Writing "x > 5" means "x is some number that is larger than 5". So anything to the right of 5 is shaded on the number line. The value 5 itself is not shaded. We use an open circle to tell the reader "do not include 5 as part of the solution set".

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Choice D: x - 7 > -2

This is another answer. It may not be as obvious as choice C, but adding 7 to both sides has us arrive to x > 5. So the same properties will apply here as they did above.