Umm N.
asked • 01/19/22i need help!!! and fyi i hattteeee PREeee ALGEBRAaaaa
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1 Expert Answer
David W. answered • 01/19/22
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There are five terms being added.
By convention, the x term would go first, the y term would go second, and the scalar term would go third.
By the Commutative Principle, you may reorder the expression:
2x + 7y + 4y + 8 + 4
Using the Associative Principle, you may group like terms and combine coefficients:
2x + (7+4)y + (8+4)
2x + 11y + 12
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Mark G.
I'll try to make this as easy as I can. First, there are 5 different numbers, or "terms" being added together. But not all the terms are in the same form, so they can't simply be added, like you might add, say, 2 + 2. One term has an x variable (2x), two terms have a y variable (7y and 4y), and two terms have no variables; they have just numbers (8 and 4.) Please note that that I have arranged all of this in a certain order. There's no rule that says you must do this, but it keeps everything organized - which makes it a lot easier to work out problems. Since x comes before y in the alphabet, we put the x-variable terms first. Next, we put the y-variable terms. Then, last, we put the no variable terms, the ones with just numbers. There' is something else that you're going to need to understand - which might not seem important, but it is. It's so important that it's a good idea to learn it now. This has to do with the words SOLVE and SIMPLIFY. These words are related, kinda-sorta, but the thing is: they don't mean the same thing. You can only SOLVE a problem if it has an equal sign in it. If the problem has no equal sign in it, you can only SIMPLIFY it. Now, let's take a look at our problem: We see right away there's no equal sign, so we can't solve it. Instead, we can simplify it. So, let's do that! First - as I said earlier - we should add the x-variable terms. Because there's only one, 2x, there's nothing more to add. So, we have 2x. Next, we add the y-variable terms, 7y and 4y. Because 7 + 4 = 11, then we know that 7y + 4y = 11y. Let's put the 11y next to the 2x. And we have this: 2x 11y OK? Now, here is where things can get very tricky, and very confusing......and it's why math problems like this can be really hard to deal with. It's also why some students hate Pre-Algebra. So, to keep that from happening, I'm going to let you in on a little secret. This secret is so useful, and it will help you so much, you'll wonder why no one ever told you before. The secret begins with a rule - a very, very, very, very important rule. And once you've learned to ALWAYS follow the rule, then you'll know the secret. And once you know the secret, Pre-Algebra becomes very easy. So, first, here's the rule: When doing math problems - whether you're simplifying or solving - you must ALWAYS, ALWAYS, ALWAYS look for the sign in front of your terms. What I mean is, look for the plus or minus sign in front of each term. This rule is very important, because it instantly tells you whether a given term is positive or negative. This is critical information, because if you get the sign wrong, you'll get the answer wrong. I repeat......if you get the sign wrong, you'll get the answer wrong. You'll get it wrong. Every. Single. Time. So, get the sign right. Here's how. And here's the secret: Every term has a sign - either positive or negative. Even if you don't see a sign at all, it still has a sign. If you see a plus sign, the term is positive. If you see a minus sign, the term is negative. But if you see NO sign in front of a term, the term is positive. Always. ALWAYS! What's more, the term that has no sign is always - ALWAYS - the first term in any problem. You'll never see that term anywhere else. Because it's always first. ALWAYS! So, don't let it fool you, and don't let it confuse you. To keep that from happening, in front of the term with no sign, draw in a big plus sign. Make it good and dark, so you know for sure it's positive. And that's the secret! That's the whole thing: Make sure every term has a sign, either positive or negative. If it has no sign, draw in a big plus sign. Good and dark. Once you've done that, in other words once every term has a sign, the rest is a breeze. OK? Now, let's go back to our problem. When we left off, we had just the two terms: 4x 11y Notice they have no signs. So, are they positive or negative? Right. They're positive. Draw in a big plus sign, slightly to the left of the term. Like this: + 4x + 11y Yes, we're almost done. Just about. All we have left is the terms with no variable, 8 and 4. 8 + 4 =- 12 Let's put the 12 in the next position, after the x-variable and the y-variable. After what we had so far: + 4x + 11y 12 The term 12 has no sign. Remember the secret? Yeppers....we know the 12 is positive. So, we have this: + 4x +11y +12 If you want to really be smart, and turn your "B" in class to an "A" - there's one more thing we should do. And it's really simple. Erase the plus sign in front of the very first term. Yes. It's that simple. 4x + 11y + 12 And, we're done! There's your answer. And your answer will be correct, EVERY SINGLE TIME, because you followed the rule, then used the secret. Follow the rule, and use the secret, Do it every time, and you can't go wrong. And you'll never be wrong again. I promise you. And why, you ask? Because, Kiddo, following the rule, and using the secret, works. Yes. It works. Every. Single. Time.02/22/22