More GED Math: Algebra

Okay, still some confusion all over about algebra. It’s tough, cuz it’s what’s called abstract. Those x’s ain’t exactly somethin’ concrete. Here’s a run-down of some basic workin’ with x’s….

Algebra’s like a puzzle. Know those puzzles where you gotta move the pieces around to make a picture? It’s like that. To find what number “x” is, you gotta move the numbers around, so that “x” is by itself on one side. And there’s rules. Here’s the key: you have to do the same thing to both sides of the equation.

So, if x + 3 = 5 and you want x by itself, you’ve got to “zero out” the + 3. To make the + 3 cancel out, you’ve got to subtract 3. That means you’ll have 3 – 3 on the side with the x, and 3 – 3 is 0, and 0 is nothing. That’s what you want… nothing with the x.

But, if you want to subtract 3 from the left side, you gotta subtract 3 from the right, too, to keep ‘em equal.

x + 3 = 5
x + 3 – 3 = 5 – 3
x + 0 = 2
x = 2

Okay, that’s the easy part. Hard part is, if you got x’s on both sides.

2x = x + 5

What do I want to do? Subtract x from both sides, to get rid of the x on the right (x – x is the same as 3 – 3 or 23 – 23…. it’s zero).

2x = x + 5
2x – x = x – x + 5
2x – x = 0 + 5
2x – x = 5

Now, what’s 2x – x? The shorthand rule is, you subtract (or add) the numbers by the x’s, and leave the x alone. “x” without a number has an invisible “1″ next to it. So:
5x – 3x = 2x
22x + 5x = 7x
x + x = 2x
5x – x = 4x

That means, if 2x – x = 5, then x = 5.

Here’s why. 5x means 5 times x. And 5 times x means x + x + x + x + x. That’s what multiplication is, a shorthand way to add a number plus itself a bunch of time.
5 × 9 = 9 + 9 + 9 + 9 + 9
5x = x + x + x + x + x

So, 2x – x means x + x – x. Two of the x’s cancel out (x – x = 0). So, it’s x + 0, or just plain x.

2 x’s minus 1 x is… 1 x. Just like if you got 2 apples and take away 1 apple, you got one apple left.

So, here’s a problem:

5x + 14 = 3x + 22

I can subtract 14 from both sides to move all the numbers to the right…
5x = 3x + 8

Now, I can subtract 3x from both sides to move all the x’s to the left…
2x = 8

The last step, since x is multiplied by 2, is divide both sides by 2 to get the x by itself….

x = 4

There ya go!