Question

hi, i need help, i dont understand this problem, how would i go about doing this? Which of the following is not an equivalent form of the compound inequality: x + 18 <= 10 and x + 18 >= 5

* A number line with a closed circle on -13, shading to the left, and a closed circle on -8, shading to the right.

*10 >= x + 18 >= 5

* -13 <= x <= -8

* A number line with a closed circle on -13, a closed circle on -8, and shading in between.

please tell me the answer and exactly how you got the answer so i can learn.

Answer 1

third one i guess

Answer 2

You should justify those answers. Simple answers do not necessarily tell how to get them in Math unfortunately.

Answer 3

:D

Answer 4

well thanks for the answer, though it would've been better to explain how you got it, for my benefit. ty anyways though

Answer 5

closing it now.

Answer 6

Well, the first thing to realize is that "x + 18 <= 10 and x + 18 >= 5" can be rewritten as "5 <= x + 18 <= 10." This is logically equivalent to (B.) if we reverse the order (10 >= x + 18 >= 5). So, (B.) is NOT the answer!

If we solve for the variable interval by subtracting 18 in both cases:
x + 18 <= 10,
x <= -8;

x + 18 >= 5,
x >= -13.

Once again, if we write this in the compact form, we get "-13 <= x <= -8," which is answer choice (C.), so (C.) is also not the answer.

We lastly observe how we plot this. The closed circles go on -13 and -8. We then shade the space between them, which is what (D.) says; so (D.) is not the answer. This is to the right of -13 and to the left of -8. It appears that (A.) is actually incorrect! We cannot shade to the right of -13 because this is the values less than -13, like -16, etc.