Solving Single Variable EquationsDate: 02/02/97 at 13:36:50 From: JAMSHID FOROUSHANI Subject: Two-step equations How do you do two-step equations? One problem is 4g + 7 = 35. I don't understand it and the math book says to do this to solve it: No. 1 Undo addition or subtraction No. 2 Undo multiplication or division My teacher explained it to us but she just said "Okay, now here's how to do it...." Then all she did was solve the problem. Susie Foroushani Date: 02/02/97 at 21:15:13 From: Doctor Steven Subject: Re: Two-step equations Hi Susie! We'll solve the equation: 4g + 7 = 35 First you subtract 7 from both sides of the equation (undoing the addition): 4g + 7 - 7 = 35 - 7 Simplify: 4g = 28. Then you divide by 4 (undoing the multiplication): 4g/4 = 28/4 Simplify: g = 7 You're done. Hope this helps. -Doctor Steven, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 02/02/97 at 22:11:14 From: JAMSHID FOROUSHANI Subject: Re: Two-step equations Thanks so much! Now I understand everything except for one part. How did you subtract 7-7? Thanks for the help. Greatfully yours, Susie Date: 02/02/97 at 22:52:31 From: Doctor Mike Subject: Re: Two-step equations Hi Susie, I read Dr. Steven's message to you. This is a very important math technique which is tricky to understand fully. But, when you do understand it, it is really powerful. I am glad to give you another explanation of it, and I think if you will compare what you heard from your teacher, and what you heard from both of us, it will be clear. Here goes: The problem you sent, "4g + 7 = 35", is an equation. You know that already, but I want to emphasize it, because it is very important for you to keep in mind that both sides of it (left and right) are EQUAL. They are the same thing, just expressed in different ways. You said what still is a puzzle is that first step, so I will concentrate on that. What Dr. Steven was doing was subtracting 7 from both sides of the equation. You can do that because (remember) the left and right parts are the same. If you start out with 2 things that are identical, and you do exactly the same to both of those things, then the results are the same. Both sides of the equation are the same. That's given; it's a guaranteed thing. So if you subtract seven from both sides, then the new left side is going to be equal to the new right side. You have another new true equation. Let's do that now. When you subtract 7 from the right side you are doing 35-7 which is 28. That's easy. When you subtract 7 from the left side you have to be just a little more sophisticated. Saying (4g+7)-7 means that you are multiplying the unknown amount "g" by 4, then adding 7 to it, and THEN subtracting seven. If you add 7 and then take away seven the result is zero, right? That's what is going on here. When Dr. Steven said to simplify 4g+7-7 to get 4g, that's what he meant. We do not know what g is yet, but whatever g is, 4g is some number. And if you add 7 to 4g and then turn right around and subtract 7 you haven't really changed anything permanently. It's still just 4g. Here is another way to write down problems like this. You no doubt are familiar with doing addition and subtraction problems by putting one over the other and the + or - sign on the second line to the left of the second number. Like this: 468 -123 ------ 345 You can do the same thing when you have a step that involves adding or subtracting the same thing with both sides: 4g + 7 = 35 -7 -7 -------- ---- 4g = 28 You can do the same thing in the next step for dividing both sides by 4, but I can't show that because my keyboard doesn't have that special symbol for division (horizontal line with a dot above it and a dot below it). Keep trying to understand the new ideas your teacher presents in class, and you will do fine. If you get into a rough spot again, then just write back to us. -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 02/03/97 at 18:20:25 From: JAMSHID FOROUSHANI Subject: Re: Two-step equations Thank you you much! I really understand now! THANK YOU! Susie |
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