# basic solving for x

• Dec 26th 2012, 03:03 PM
sweezy
basic solving for x
problem one:
ax = bx +c
x = c/(a-b)

problem two:
ax - b = cx + d
x = (d+b)/(a-c)

I'm pretty lost here, and would appreciate any help.
• Dec 26th 2012, 03:42 PM
Prove It
Re: basic solving for x
\displaystyle \begin{align*} a\,x &= b\,x + c \\ a\,x - b\,x &= c \\ x\left( a - b \right) &= c \\ x &= \frac{c}{a - b} \end{align*}

Can you follow a similar process to solve the second one?
• Dec 26th 2012, 05:10 PM
sweezy
Re: basic solving for x
ax - b = cx + d
ax = cx + (d + b)
ax - cx = (d + b)
x (a - c) = (d + b)
x = (a - c)/(d + b)

Thank you, it's clear to me now even if it doesn't seem so without the tex tags.
• Dec 27th 2012, 10:39 AM
earboth
Re: basic solving for x
Quote:

Originally Posted by sweezy
ax - b = cx + d
ax = cx + (d + b)
ax - cx = (d + b)
x (a - c) = (d + b) <--- up to this line evrything is fine, but then .....
x = (a - c)/(d + b)

Thank you, it's clear to me now even if it doesn't seem so without the tex tags.

x (a - c) = (d + b) ........ You now have to divide by (a - c) which yields:

x = (d + b) / (a - c)