anonymous
  • anonymous
5x(3x+2)-6 < 4X(2X-5) +12
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Hello
anonymous
  • anonymous
Do you have any guesses on how to start this problem?
anonymous
  • anonymous
I multipy 5x 15+10-6< 4x 12x-20+12, I am not good at all with algebra.

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anonymous
  • anonymous
You were indeed correct to start off by distributing. But we have a couple minor errors with your distribution, however.
anonymous
  • anonymous
When you multiply 5x times 3x, what do you get?
anonymous
  • anonymous
15
anonymous
  • anonymous
Actually, you get 15x^2. The x's multiply with each other. But the 5*3 was spot on.
anonymous
  • anonymous
okay, thanks!
anonymous
  • anonymous
Do you see how that works?
anonymous
  • anonymous
Do you see how that works?
anonymous
  • anonymous
Alright, now let's try to multiply the 5x and the +2 together.
anonymous
  • anonymous
5x + 2 -7
anonymous
  • 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
  • anonymous
Yes, 5x2+10
anonymous
  • anonymous
Mm.. Not quite. Remember, the x is a variable, not the same as a multiplication symbol. 5x * 2 = 10x
anonymous
  • 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
  • anonymous
Okay I understand
anonymous
  • 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
  • anonymous
Yes!
anonymous
  • 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
  • anonymous
Okay I am following!
anonymous
  • anonymous
Cool, can you distribute on the right side then? 4X(2X-5) +12
anonymous
  • anonymous
yes 20x^4 +10
anonymous
  • 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
  • anonymous
8x^2 +12
anonymous
  • 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
  • anonymous
4x8-5+3
anonymous
  • 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
  • anonymous
would it be 1x
anonymous
  • 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
  • anonymous
20
anonymous
  • 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
  • anonymous
20x's
anonymous
  • 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
  • anonymous
Yes it does, thank you!
anonymous
  • 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
  • anonymous
15x2+10x-6 < 20x2-20x+12 -15x+6 20x-12
anonymous
  • 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
  • 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
  • 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
  • anonymous
I added six to both sides to get +18 on the right side. The rest is correct :)
anonymous
  • anonymous
Now, are you familiar with the quadratic equation?
anonymous
  • 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
  • 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
  • anonymous
Oh wait. I lie.
anonymous
  • anonymous
Okay
anonymous
  • anonymous
I screwed up my math somewhere. The system is true when: -4.819 < X < 0.533
anonymous
  • anonymous
And that's the answer.
anonymous
  • anonymous
Okay thank you!!!! I am going to print out this information and study it and I will practice other problems. Thanks again!!!!
anonymous
  • anonymous
No problem Sorry I couldn't be more clear.

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