Date: 12/12/97 at 00:43:46 From: Jared Subject: Algebra (equations) What is the answer to the problem: 15-(5m-4) = 34? I need to know how to do the 15- part - that is where I am having trouble. Please just give me the first couple of steps. Thank you.
Date: 12/29/97 at 10:31:29 From: Doctor Mark Subject: Re: Algebra (equations) Hi, Jared - Problems like this are incredibly easy to do once you know the secret. And here is the secret: If you have a minus sign in front of (to the left of) a pair of parentheses, remove the parentheses by *changing all the signs* of whatever is *inside* the parentheses. So in your problem, you would find out what - (5m-4) is by changing all the signs in the quantity 5m - 4 (which is what is inside the parentheses). In doing this, you have to remember that the 5m has a secret "+" sign in front of it, which is not usually written. So, - (5m - 4) = - ([+]5m - 4) = - 5m + 4. Do you see how the + 5m got changed to - 5m, and the - 4 got changed to + 4? Do you agree that all the signs of the thing inside the parentheses got changed when we removed the parentheses? Once you have removed the parentheses, then you just collect terms. So 15 - (5m - 4) = 15 - 5m + 4 = - 5m + 15 + 4 = - 5m + 19. (Did you remember that the 15 was really just + 15? Another secret "+" sign!) I'll have to admit that remembering to change that last (-) sign [the one in front of the 4] when removing parentheses having a (-) sign on the left is hard. I forget it myself sometimes, and boy, do I feel like an idiot when I do! Now back to the equation (this was just the left side)... 15 - (5m - 4) = 34. This becomes, from above, - 5m + 19 = 34. Now add 5m to both sides to get 19 = 34 + 5m And subtract 34 from both sides to get 19 - 34 = 5m which becomes - 15 = 5m. Now turn it around so it looks normal: 5m = - 15, and divide both sides to get (finally!) m = - 3 You may have noticed that I got the m-term on the right. This was so I did not have to divide by a negative number, which I find distasteful. The only other thing you have to remember to do problems like this correctly is that you should always write subtractions of "like" terms last. Here is an example: - 4x - 3 - (8 - 7x) = - 4x - 3 - 8 + 7x = 7x - 4x - 3 - 8 = 3x - 11 Notice two things here: 1) when we removed the parentheses, we changed all the signs of the thing inside the parentheses: 8 - 7x --> - 8 + 7x, i.e., - (8 - 7x) = - 8 + 7x. 2) we wrote - 4x + 7x = 7x - 4x i.e., we put the subtraction "last" (on the right). This idea of "put subtractions last" is just so that we can avoid mistakes. I hope this was of help, Jared, and make sure you write back if you have any other questions. -Doctor Mark, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.