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Do you have any guesses on how to start this problem?
I multipy 5x 15+10-6< 4x 12x-20+12, I am not good at all with algebra.
You were indeed correct to start off by distributing. But we have a couple minor errors with your distribution, however.
When you multiply 5x times 3x, what do you get?
Actually, you get 15x^2. The x's multiply with each other. But the 5*3 was spot on.
Do you see how that works?
Do you see how that works?
Alright, now let's try to multiply the 5x and the +2 together.
5x + 2 -7
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?
Mm.. Not quite. Remember, the x is a variable, not the same as a multiplication symbol. 5x * 2 = 10x
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 *.
Okay I understand
Great. So if you want to double (or multiply by two) your five X's, you now have 10 X's. Is that clear?
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
Okay I am following!
Cool, can you distribute on the right side then? 4X(2X-5) +12
yes 20x^4 +10
Hmm.. Let's try this together. 4X(2X) Can you do this for me? Remember what I said above about multiply two Xs together.
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?
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?
would it be 1x
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?
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?
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. :)
Yes it does, thank you!
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?
15x2+10x-6 < 20x2-20x+12 -15x+6 20x-12
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
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.
You subtracted 2 on both sides to get the answer 18 and combined like terms 15x 20x and 5x and added 10+20 = 30.
I added six to both sides to get +18 on the right side. The rest is correct :)
Now, are you familiar with the quadratic equation?
Yes I understand somewhat, however I will continue to practice and study for a better understanding. Thank you so much for your help!
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.
Oh wait. I lie.
I screwed up my math somewhere. The system is true when: -4.819 < X < 0.533
And that's the answer.
Okay thank you!!!! I am going to print out this information and study it and I will practice other problems. Thanks again!!!!
No problem Sorry I couldn't be more clear.