Answer:
H. -5 + x < -1
Explanation:
Okay so let's first look at our little graph thing. What is it saying? It's telling us that what ever x is, it is NOT 4 (because the circle is not filled in) and it is less than 4 (because it's all shaded in before 4). Now that we know this, lets look at our possible answers.
F. x - 3 < 7
Now, for all of these possible answers, we can solve them exactly like normal equations (like x - 3 = 7).
x - 3 < 7
[add 3 to both sides to leave the x by itself]
x < 10
Whoa, that's not right! We don't even have 10 on our graph, so F is out of the running.
G. x + 6
10
Okay, let's work smarter, not harder here. So we can see that there is a greater than or equal to sign there. So even if we solve it and we get 4 as the answer, our graph doesn't include 4. So we can throw this answer out right away.
H. -5 + x < -1
Solve like a normal equation in the first one.
-5 + x < -1
[add 5 to both sides to leave the x by itself]
x < 4
Hey! We got something! So let's read this with words. So whatever x is, it does not include 4, and is less than 4. So now looking back on our first brainstorm of the graph, this is in line with what we want.
So this is the answer! Yay!
Just for fun let's look at the last possible answer.
I. x - 8 > -4
Again, solve like a normal equation.
x - 8 > -4
[add 8 to both sides to leave x by itself]
x > 4
Oh! Another 4! But this time the sign is different. Let's read it again with words. So whatever x is, it does not include 4 (ok, good), and is greater than 4 (oh, not good). Our graph showed us that x is less than 4. So this answer is not the answer.
So again, we keep H. as our correct answer.