Here’s a problem that Lyndia sent in, since she was havin’ trouble with it:
3x = 7 – 4x
You wanna figure out what “x” is equal to The problem comes in when you have a number befo’ the x, and need to get all the “x”es on the same side. Think of it this way… you don’t just got one x, you got four x’s. So, you gotta move all 4 x’s to the other side. In other words, think of “4x” as all going together.
3x = 7 – 4x
Add 4x to both sides to get rid of the x’s on the right…because you have to get rid of all four x’s.
3x + 4x = 7 – 4x + 4x
The -4x and the +4x cancel each other on the right side… and on the left, 3x + 4x = 7x. Think of it like that’s how many x’s you got… 3 x’s (x +Â x + x) plus 4 x’s (x + x + x + x) gives you 7 x’s (x + x + x + x + x + x + x).
7x = 7
Now, if the 7 goes with the x, how do you get rid of it? You can, because what it’s really saying is 7 times x. 7 times x is the same as (x + x + x + x + x + x + x) is the same as 7x. Just like 7 times 3 is the same as (3 + 3 + 3 + 3 + 3 + 3 + 3), and could be written 7(3). Divide by 7 on both sides to get:
x = 1
Let me know if this gives you any more problems!
For more information about the GED test and GED test preparation, visit the GED Academy at http://www.passGED.com.
Related Articles
4 users responded in this post
This is very tough bro ! LOL !
just don’t get it
Algebra’s like a puzzle. Know those puzzles where you gotta move the pieces around to make a picture? It’s like that. 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 = 0 on the side with the x, and 0 is nothing.
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 – 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 = x – x + 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 x 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. 2 x’s minus 1 x is… 1 x. Just like if you got 2 apples and take away 1 apple.
So… 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…
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!
Sounds easy when you explain it like that. But as soon as I am sitting in front of a different Algebra task, my brain just shuts down because it all just doesn’t make sense.
Leave A Reply
Please Note: Comment moderation maybe active so there is no need to resubmit your comments