Starting algebra and I have a problem.

[Oochy]

Okay, maybe I just totally missed somthing somewhere, but I encountered a problem while learning "Combination of Terms Equations".

Here is how they work the problem:

6x - 2x + 6 = x -2x -16
4x + 6 = -x + 16
-6 + -6
-------------------
4x = -x + 10
+x = +x
---------------
5x = 10
5x = 10
5----5
---------------
x = 2
​

Now, can you explain how they did this? What happened to the '2' and where did the negitive 'X' come from, etc?? Show me how to work this please, because they don't. It seems like they're pulling numbers out of thin air. :grumpy:

 

[matt grime]

no, they're doing algebraic manipulation:

i have three times a number, say and i add five times the same number to it, what do i have? 8 times the same number: 3x+5x=(3+5)x=8x

now you say what happened to the 2, well, i can see 3 of them in there, which one do you mean?

just treat x as a number and manipulate it according to the rules of arithmetic

 

[jcsd]

6x - 2x + 6= x - 2x - 16

6x - 2x = 4x and x - 2x = -x therefore we can reduce our equation to:

4x + 6 = -x + 16

add -6 to both sides (i.e. takeaway 6 from both sides)

4x = -x + 10

add x to both sides:

5x = 10

divide both sides by 5:

x = 2

 

[Oochy]

x - 2x = -x

Why do we loose the 2 though? When you subtract by x does it always make it negitive?

 

[TALewis]

x - 2x can be written like this:

1x - 2x

Replace x with "apple:"

1apple - 2apples

You're left with -1apple. That's why:

x - 2x = -x

You don't really have to think about what x is doing there. Just think about 1 minus 2:

1 - 2 = -1

 

[Oochy]

Okay, thanks! Now it makes sense!

Thanks guys!

 

[addman]

shouldnt it be -16 on the second line?

 

[killerinstinct]

Either copied the problem wrong or did the entire equation wrong! 1st line and 2nd line don't match!

 

[FlatlineLemon]

shouldnt it be -16 on the second line?

thats the first thing i said,lol, i was thinking "hmmm...that could be your problem right there"

 

[robert Ihnot]

A false change of sign!

shouldnt it be -16 on the second line?

You are exactly right! The first equation certainly will not balance with x=2.