# solve this equation for x

• May 22nd 2010, 09:40 AM
irichi09
solve this equation for x
How do you do this?

solve for x:

ax = bx - c

Thank you.
-r
• May 22nd 2010, 09:52 AM
Anonymous1
$ax = bx - c$

$\implies ax- bx = -c$

$\implies x(a- b) = -c$

$\implies \boxed{x=-\frac{c}{a-b}}$
• May 22nd 2010, 10:12 AM
freetibet
solve for x:

ax = bx - c

solution: ax - bx = c
(a -b)x = c
x = c/(a - b)
• May 22nd 2010, 11:07 AM
correct solution
This is the correct solution:
$

ax = bx - c
$

$

\implies ax- bx =-c
$

$

\implies x(a- b) =-c
$

$

\implies \boxed{x=-\frac{c}{a-b}}
$
• May 22nd 2010, 04:46 PM
irichi09
thank you for helping
it seems so easy when you see the solution, but not so easy when your making holes in the wall with your forehead.(Coffee)
• May 22nd 2010, 05:38 PM
Quote:

Originally Posted by irichi09
it seems so easy when you see the solution, but not so easy when your making holes in the wall with your forehead.(Coffee)

To protect the wall from your forehead, you need to know how to think it through.

Solve for x means we are being asked to write x=?

What we are given contains x in 2 places, on either side of the equal sign.
When both sides are equal we can perform the exact same operation to both sides.

For instance 5=5

If we subtract 3 from both sides we'll have 5-3=5-3 which is 2=2

The sides may not be what they were originally but they are still equal.

Hence

$ax=bx-c$

has x on both sides.
To get the x's on the same side, subtract bx from both sides,
the two sides will still be equal...

$ax-bx=bx-bx-c$

$bx-bx=0$

therefore we have

$ax-bx=-c$

If you have 5 boxes of apples, 20 apples per box
and you give 3 boxes to your sister, how many apples will you have ?

$5(20)-3(20)=(5-3)(20)$

You can calculate 100-60=40 or 2(20)

Hence we get x in one place by factorising as above.

$ax-bx=-c$

$x(a-b)=-c$

This is "x multiplied by both a and -b".

To move the (a-b) away from the x, to leave x standing alone,
we divide both sides by (a-b), just as

$3x=6\ \Rightarrow\ \frac{3x}{3}=\frac{6}{3}$

$\frac{3}{3}x=\frac{6}{3}$

As $\frac{3}{3}=1$

this is

$x=2$

Hence

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

$\frac{(a-b)}{(a-b)}=1$

$x=-\frac{c}{a-b}=\frac{c}{b-a}$
• May 22nd 2010, 10:26 PM
brumby_3
Nice explanation Archie!