# Subject of a linear equation

• Feb 19th 2008, 09:08 PM
stellina_91
Subject of a linear equation
Rearrange the formula so that the pronumeral written in square brackets is the subject.

c = 7 + 2d [d]
/
5 - 3d

Do you need to multiply 5 - 3d to the left side so that, c(5 - 3d) = 7 + 2d?

If so I ended up with 5c - 3cd = 7 + 2d
-5c -5c
-3cd = 7 + 2d - 5c

Thanks a lot.
• Feb 19th 2008, 10:29 PM
earboth
Quote:

Originally Posted by stellina_91
Rearrange the formula so that the pronumeral written in square brackets is the subject.

c = 7 + 2d [d]
/
5 - 3d

...

I assume that you want to solve for d:

$\displaystyle c = \frac{7+2d}{5-3d}$ ......... get rid of the denominator by multiplying by (5 - 3d):

$\displaystyle c(5 - 3d) = 7+2d$ ......... expand the bracket:

$\displaystyle 5c - 3cd = 7 + 2d$ ......... collect all terms containing d at the RHS, the other at the LHS:

$\displaystyle 5c - 7 = 2d + 3cd$ ......... factor out d:

$\displaystyle 5c - 7 = (2 + 3c) d$ ......... divide both sides by the bracket:

$\displaystyle \frac{5c-7}{2+3c} = d$ ......... that's it!

I've done this problem extensively so that you have an example to do all similar questions.
• Feb 19th 2008, 10:34 PM
stellina_91
Thank you so much for your help, it's greatly appreciated!!!