5x(3x+2)-6 < 4X(2X-5) +12

- anonymous

5x(3x+2)-6 < 4X(2X-5) +12

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- anonymous

Hello

- anonymous

Do you have any guesses on how to start this problem?

- anonymous

I multipy 5x 15+10-6< 4x 12x-20+12, I am not good at all with algebra.

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## More answers

- anonymous

You were indeed correct to start off by distributing. But we have a couple minor errors with your distribution, however.

- anonymous

When you multiply 5x times 3x, what do you get?

- anonymous

15

- anonymous

Actually, you get 15x^2. The x's multiply with each other. But the 5*3 was spot on.

- anonymous

okay, thanks!

- anonymous

Do you see how that works?

- anonymous

Do you see how that works?

- anonymous

Alright, now let's try to multiply the 5x and the +2 together.

- anonymous

5x + 2 -7

- anonymous

5x(3x+2)-6
Hmm.. Not quite. Maybe you don't know where I am talking about. In the above phrase, will you take the 5x and multiply it with the 2 in the parenthesis?

- anonymous

Yes, 5x2+10

- anonymous

Mm.. Not quite. Remember, the x is a variable, not the same as a multiplication symbol.
5x * 2 = 10x

- anonymous

Oh, and by the way, * is the computer symbol for multiplication. And that's the reason why, we don't want to get confused about whether it's a letter x or an operation so we use *.

- anonymous

Okay I understand

- anonymous

Great. So if you want to double (or multiply by two) your five X's, you now have 10 X's. Is that clear?

- anonymous

Yes!

- anonymous

So on the left side we went from:
5x(3x+2)-6
To:
15x^2 + 10x - 6
Following? Now we'll want to do distribute on the right side:
4X(2X-5) +12

- anonymous

Okay I am following!

- anonymous

Cool, can you distribute on the right side then?
4X(2X-5) +12

- anonymous

yes 20x^4 +10

- anonymous

Hmm.. Let's try this together.
4X(2X)
Can you do this for me? Remember what I said above about multiply two Xs together.

- anonymous

8x^2 +12

- anonymous

Excellent, very very good. Now you left out one last part for the right side:
4X(2X-5) +12
Can you do the 4x * -5?

- anonymous

4x8-5+3

- anonymous

I'm afraid not.
4x * -5 = -20x
Pretend that an X is an item. Don't even bother calling it a variable. Now, I have 4 Xs. If I have 4 Xs and I multiply my Xs by negative five, how many Xs do I have?

- anonymous

would it be 1x

- anonymous

Hmm.. Let's try something a little different.
If I have 4 pennies and you said that you could multiply my pennies by five, by the end of it, how many pennies would I have?

- anonymous

20

- anonymous

Exactly. Now, pretend that my pennies were really just little X's all along. Not a letter, not a variable, a real X, something I could hold in my hands. I'll ask you the same question.
If I have 4 X's in my hand and you said you could multiply my X's by 5, how many X's would I have?

- anonymous

20x's

- anonymous

Great, does that make it a little more clear? That is how you should approach these problems when multiplying X's. Just pretend they are just labels. :)

- anonymous

Yes it does, thank you!

- anonymous

So we had this:
5x(3x+2)-6 < 4X(2X-5) +12
And turned it into this:
15x^2 + 10x - 6 < 20x^2 - 20x + 12
When we solve algebraically, we'll want everything that has that nasty X on the same side of the inequality. Do you know how you might accomplish that?

- anonymous

15x2+10x-6 < 20x2-20x+12
-15x+6 20x-12

- anonymous

Afraid not.
We'll want to do:
15x^2 + 10x - 6 < 20x^2 - 20x + 12
+6 -20x^2 +20x +6
To get:
15x^2 +10x - 20x^2 + 20x < 18

- anonymous

From there we can combine like terms:
The x^2s can combine.
15x^2 - 20x^2 = -5x^2
The X's can combine.
10x + 20x = 30x
So we end up with:
-5x^2 + 30x < 18.

- anonymous

You subtracted 2 on both sides to get the answer 18 and combined like terms 15x 20x and 5x and added 10+20 = 30.

- anonymous

I added six to both sides to get +18 on the right side. The rest is correct :)

- anonymous

Now, are you familiar with the quadratic equation?

- anonymous

Yes I understand somewhat, however I will continue to practice and study for a better understanding. Thank you so much for your help!

- anonymous

It's no problem. I just wish I could be a little more clear, it's hard to do that with just text.
Anyways, we'll use the quadratic equation, first we have to make the equation equal to 0:
-5x^2 + 30x < 18
-18 -18
-5x^2 + 30x -18 < 0
And then plug in the A, B, and C values into the quadratic equation:
-b plus/minus sqrt of b^2 - 4AC all divided by 2A
- 30 plus/minus sqrt 30^2 - 4*-5*-18, all divided by 2(-5) = 16.905 and 133.09. Those are your values of X and those are the answers. Two of them.

- anonymous

Oh wait. I lie.

- anonymous

Okay

- anonymous

I screwed up my math somewhere.
The system is true when:
-4.819 < X < 0.533

- anonymous

And that's the answer.

- anonymous

Okay thank you!!!! I am going to print out this information and study it and I will practice other problems. Thanks again!!!!

- anonymous

No problem Sorry I couldn't be more clear.

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