Solve for X
Date: 10/09/1999 at 15:52:22 From: Jenna Subject: I don't understand Dear Dr. Math, I'm so confused! I have my math book in front of me and I don't understand how to do a problem like this: 4x - 1/2 = -3/2 Could you help me and explain it so that I can understand? My book just confuses me.
Date: 11/03/1999 at 21:55:22 From: Doctor Sandi Subject: Re: I don't understand Hi Jenna, Don't worry, we'll get to the bottom of it and work it out. Math books can be pretty confusing because they use math language, which is a whole new concept in itself that needs to be learned along the way and makes things seem confusing. I would encourage you to persevere with your math book though - even though it is confusing, if you keep on reading it and trying to follow the examples in the book, it will get easier to understand the more you read it. And, as you get into higher grades with math, if you can understand a math book, believe me, you'll do a lot better than you would otherwise. What I will do, Jenna, is make up an equation similar to yours, and we'll work through it, find the answer, and then you'll be able to use the same process to find the answer to your problem on your own. But before I go on, let me say something about the way you wrote your question. You need to put brackets around the fractions; otherwise someone might think it could mean (4x-1)/2 = (-3/2). I'm hoping that I've guessed right though, and have interpreted your question correctly. Let's work through this one: 2x - (1/2) = (-5/2) We need to find the value of x, so we have to get the 2x on its own. The first thing to do is to take the -(1/2) over to the other side. Do you remember that when you take a negative number over to the other side of an equation, it becomes a positive number? If the number is negative, to move it to the other side of the equation, the negative needs to be "undone" and it will then become a positive. So then we have: 2x = (-5/2) + (1/2) You could work this out on your calculator, but since they both have the same denominator (number on the bottom of the fraction) you could say -5 + 1 = -4, so 2x = -4/2, which cancels down to 2x = -2. Now let's have a look at the x again. It is nearly on its own but not quite. We need to get rid of the 2 that is multiplying the x. We need to move it to the other side and "undo" the multiplying action. What do we need to do with the 2 when we apply it to the other side to "undo" the multiplication? Yes, you're right, we'll divide. Then we have: x = -2/2 = -1 There, it wasn't really that hard in the end when you worked through it with me was it? I hope not, anyway. But if it was, take heart because EVERYTHING is hard to do when we first learn how to do it. So, my advice to you would be to do as many of these kinds of equations as you possibly can, and the more you do, the easier it will get, I promise. Something that also helps immensely is that now that you have found the value of x, you could put it back into the original equation to see if it all checks out. Then you know that you're right (or wrong). We'll do it with this one: 2x - (1/2) = (-5/2) So if we write 2(-1)-(1/2) = (-5/2) we have put the -1 in place of the x and we're hoping that when we work through it that it does indeed solve to be (-5/2). Okay, 2 times -1 = -2. -2 - (1/2) = -(5/2). Yes! Now you know that the answer that we found for x was right, because when we put x = -1 back into the equation and solve it we get -(5/2) as the answer, just as it's meant to be. This is good to remember in exams (if you have time). You can often check your answers by working backward. Here are some links that you might like to have a look at. You'll see that they are questions that other people have asked Dr Math together with the answers that they received. Algebra http://mathforum.org/dr.math/tocs/algebra.middle.html Equations http://mathforum.org/dr.math/tocs/equation.middle.html Negative Numbers http://mathforum.org/dr.math/tocs/negative.middle.html Word Problems http://mathforum.org/dr.math/tocs/wordproblem.middle.html If you click on "Back to Middle School Level" on these pages you'll see that there are many more topics, and if you click on "Search Dr Math" you'll be able to search the whole archive for whatever topic you want. In the meantime though, if you don't understand how we did the equation above and you have more questions about this type of thing or any questions about any other areas of mathematics that you would like to ask, we'd like to hear from you. Just email us and we'll try to help. - Doctor Sandi, The Math Forum http://mathforum.org/dr.math/
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