How do you do this?
solve for x:
ax = bx - c
Thank you.
-r
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
$\displaystyle ax=bx-c$
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...
$\displaystyle ax-bx=bx-bx-c$
$\displaystyle bx-bx=0$
therefore we have
$\displaystyle ax-bx=-c$
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 ?
$\displaystyle 5(20)-3(20)=(5-3)(20)$
You can calculate 100-60=40 or 2(20)
You get the same answer.
Hence we get x in one place by factorising as above.
$\displaystyle ax-bx=-c$
$\displaystyle x(a-b)=-c$
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
$\displaystyle 3x=6\ \Rightarrow\ \frac{3x}{3}=\frac{6}{3}$
$\displaystyle \frac{3}{3}x=\frac{6}{3}$
As $\displaystyle \frac{3}{3}=1$
this is
$\displaystyle x=2$
Hence
$\displaystyle \frac{x(a-b)}{(a-b)}=-\frac{c}{(a-b)}$
$\displaystyle \frac{(a-b)}{(a-b)}=1$
$\displaystyle x=-\frac{c}{a-b}=\frac{c}{b-a}$