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 Originally Posted by spoonitnow
The following is the easiest way I know how to explain the basics of solving equations. Please let me know if these examples help or not so that I can make better ones in the future.
We'll have to use examples with larger numbers that you can't just do in your head for this to work. In all of these examples, we're going to solve for x. (That just means figuring out what number x is.) I used some color to make it easier to see what's happening in these three examples.
The Rule You Need to Know: You can do something to one side of the equation as long as you do it to the opposite side of the equation. (The two sides are the left and right of the equals sign.)
Example 1: 372x = 36456
Remember that 372x just means 372 times x. We would like to have x = "a number," but the multiplication by 372 is keeping us from having that. We can get rid of this problem by dividing the left side of the equation by 372. To keep the equation balanced, we also have to divide the right side of the equation by 372.
372x/372 = 36456/372
x = 98
Example 2: x + 14.68 = 43.93
We would like to have x by itself on the left side of the equation. Obviously, the addition by 14.68 is keeping us from having that. We can get rid of it by subtracting 14.68 from the left side of the equation. Since we're going to do it to the left side, we also have to do it to the right side. Here's what we get:
x + 14.68 - 14.68 = 43.93 - 14.68
x = 29.25
Example 3: 2.2x + 5.467 = 25.091
This example is just barely more complicated than the first two. Again, we'll want to get x by itself. To do so, we'll need to get rid of the addition by 5.467 and the multiplication by 2.2. We can only get rid of one at a time, so we'll start with getting rid of the addition by subtracting 5.467 from both sides.
2.2x + 5.467 - 5.467 = 25.091 - 5.467
2.2x = 19.624
We're now one step closer to having x by itself, so we have made progress. Now we'll divide both sides by 2.2 to get rid of the multiplication.
2.2x/2.2 = 19.624/2.2
x = 8.92
If you can understand the thought process and the strategy used to get x by itself in examples like these, then you're only a couple of rules away from having a decent enough understanding of basic algebra to do things like solve for balanced strategies.
YES! YES! YES! I actually understand everything you just wrote.
Let me try;
3.8x + 7.975 = 54.698
OK, so first we have to get x by itself. First thing is to get rid of the 7.975, we do this by subtracting 7.975 and we have to do this from both sides.
3.8x + 7.975 - 7.975 = 54.698 - 7.975
3.8x = 46.723
Now to get x by itself, we can divide both sides by 3.8.
3.8x/3.8 = 46.723/3.8
x = 12.30
I hope I have got that right.
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