# Thread: Simple Equation That Is Mind-Boggling For Some Reason

1. ## Simple Equation That Is Mind-Boggling For Some Reason

I am a college freshmen who isn't currently enrolled in an algebra class due to my low score on my testing. I am teaching myself algebra using E-Z algebra and I have stumbled upon a frustrating equation and I searched for a math help forum and found this site. I will probably have many more questions in the future so I appreciate any help that can be given.

Here is the problem

ax = bx + c (solve for x)

so I subtracted bx from both sides and got: a -bx = c

then i divided both sides by a-b

I ended up with: x = c/a-b

My question is this: if I subtract bx from both sides in step 1, how does that translate to a -bx? Why wouldn't it be ax - bx or a - b and the -x cancels out the other x? I'm seriously confused...I'm sure the explanation is real simple though.

2. ax=bx+c.

Both sides are equal,
If we change one, they will still be equal if we change both in the exact same way.

Subtract bx from both sides to bring the x parts together.

ax-bx=bx-bx+c.
ax-bx=c.

X is common in ax-bx, so we write it as x(a-b).

It's like 5(3)-3(3)=(5-3)3 or 7(4)-2(4)=(7-2)4.

So, x(a-b)=c.

Now, divide both sides by (a-b).

$\displaystyle x\frac{(a-b)}{(a-b)}=\frac{c}{(a-b)}$

$\displaystyle x=\frac{c}{a-b}$

3. thank you for the quick reply, I appreciate the help

one last question: if ax - bx = c why do you simplify the equation to x = (a-b)? I understand the (a-b), but how would you end up with a singular x? When you simplify ax - bx how would you get only 1 x out of that equation instead of 2x? Sorry if I seem stupid, but I am just trying to comprehend this 100%.

4. You have the right attitude to this...

suppose you have 7 bags of apples, x=5 apples in each bag.
You give 4 bags to your friend.

You now have 7x-4x left for yourself,
which is of course 3 bags left,
but we can write it as (7-4)x or (7-4)5 apples.

If I have 8 boxes of books, 10 books in each box,
I put 3 boxes in the attic, I have 5 boxes left.

I have 5(10)=50 books downstairs or (8-3)10.

We can place common items in brackets,
it's known as factoring or factorising, it's just grouping common terms.

5. nice, thanks for the detailed response!