Question 22547: hi i need help on solving linear equations. i know nothing about them. im in 8th grade and ive gotten help with stuff before on your site but i didnt understand so please use 8th grade terms thank you
Answer by ilana(307)   (Show Source):
You can put this solution on YOUR website! OK, that's kind of a general question, but I'll give it a try.
Suppose you have the linear (it is linear because there's no 4^2, for example) equation 3x+17=38.
To "solve" this equation, we mean find what x is to make this a true statement.
Now, we begin by looking at what kinds of things (operations) we are doing to the numbers. Here, we have multiplication and addition. We first look at addition and subtraction, and then multiplication and division when solving linear equations. So let's look at the addition part, +17.
Our goal is to have the equation look like "x=(some #)" so we want all of the numbers in the problem to be separated from the x, on the other side of the = sign.
The "opposite" of addition is subtraction, so we subtract 17 from both sides of the = sign. (If we do something to one side, we must do it to the other, so the equation says the same thing. For example, if we have 2=2, saying 2-17=2 is false, but saying 2-17=2-17 is still true. We want everything we say to stay true.)
OK, so we have 3x+17-17 = 38-17.
38-17 is just a number (think back to regular little kid math), so we can say:
3x+17-17 = 21.
Now, remember why we subtracted 17? It was to get rid of the +17. And it worked, since 17-17=0. SO we have 3x = 21.
Now, we have only multiplication. The opposite of multiplication is division, so we see "times 3" and we divide by 3 (both sides again).
So we have (3x)/3=21/3.
3, times x, divided by 3, is the same as (3/3) times x, which is 1*x, which is x.
21/3=7 (again, think back to little kid math).
So, we have x=7. This is the "solution".
If we want to test if it's right (this is usually a good idea), we can "plug it in". We started with 3x+17=38. Now, we think x=7. So try it.
That would mean (3*7)+17=38. So 21+17=38. So 38=38.
This is true, so YAY, WE'RE RIGHT!!:)
Hope this helped, best of luck!
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