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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Sabrina (Customer)

[00:00:00] Use a graph to slove the inequality

Anita G (Tutor)

[00:00:10] Welcome to Tutor.com !
Let's get started.

[00:00:18] is that an 8 on the numerator?

Sabrina (Customer)

[00:00:28] yes

Anita G (Tutor)

[00:00:31] Awesome.

[00:01:10] now, let's look at this: do you know how to graph 8/(x^2+4)?

[00:01:35] I mean 8/(x^2+1)

Sabrina (Customer)

[00:01:38] dont we aave to get =to 4

[00:01:42] i mean 0

Anita G (Tutor)

[00:01:58] Yes, but I thought the problem said to graph to solve the inequality

[00:02:04] But sure, we can do that

[00:02:17] Actually, if we're going to do that, then there is a much easier way

[00:02:37] how do we get rid of the fraction on the left side?

[00:02:47] how do we move the x^2+1 to the right side?

Sabrina (Customer)

[00:03:14] subtract

Anita G (Tutor)

[00:03:19] Not subtract.

Sabrina (Customer)

[00:03:24] factor?

Anita G (Tutor)

[00:03:39] Right now the left side is 8 divided by (x^2-1)

[00:03:41] right?

Sabrina (Customer)

[00:03:46] yes

[00:03:50] oh mulitply

Anita G (Tutor)

[00:03:55] You got it!

[00:03:59] and what do we get?

[00:04:49] Sure

[00:04:53] how do we simplify the right side?

[00:05:12] Correct

[00:05:18] Now, how do we make the left side 0?

[00:06:17] Correct. but still leave the >=

[00:06:31] Correct

[00:06:39] Now what do we do?

Sabrina (Customer)

[00:06:47] plug 0 in the x

[00:06:53] and 2 in the x

Anita G (Tutor)

[00:06:57] Sure

[00:07:10] Actually, this is the algebraic method, not the graphical method

[00:07:23] So, we can just keep going further

Sabrina (Customer)

[00:07:30] then what do we do

Anita G (Tutor)

[00:07:57] So we get this answer

[00:08:00] does that make sense?

[00:08:23] Actually hold on a second

[00:08:28] You forgot the x^2 here:

[00:09:09] what are our critical points now?

[00:09:11] not just 1

Sabrina (Customer)

[00:09:45] 1 and 1

Anita G (Tutor)

[00:09:49] 1 and -1

[00:09:51] right?

Sabrina (Customer)

[00:09:54] right

Anita G (Tutor)

[00:10:06] Okay, would you like to do it this way or would you like to do it the graphical way?

Sabrina (Customer)

[00:10:28] i have to do it the graphical
way

Anita G (Tutor)

[00:10:33] Correct

[00:10:37] So, we have to stop at this:

[00:11:02] Now, how can we simplify this?

[00:11:10] we can factor out 4 from the right side, right?

[00:11:32] square it

[00:11:40] Not there

[00:11:44] the x is still squared

[00:11:54] Does that make sense?

[00:12:03] Correct

[00:12:14] Now, we can divide both sides by 4 to get rid of the 4

[00:12:37] Does that make sense?

Sabrina (Customer)

[00:12:42] yes i got it

Anita G (Tutor)

[00:12:45] awesome.

[00:12:56] Now we just graph it and see when the graph is under y=0

Sabrina (Customer)

[00:13:10] i can do that
thanks