# Simplifying Linear Equations

• Jun 2nd 2008, 08:47 AM
cmf0106
Simplifying Linear Equations
This is some steps into the equation

But I am having difficulty simplifying this
$\displaystyle x- \frac{3}{2}x = -8\frac{1}{2}$

The author shows the above simplified as
$\displaystyle -\frac{1}{2}x = -8 \frac{1}{2}$

Can you adjust assume X = 1 and do $\displaystyle 1 - 3/2$ thus equaling $\displaystyle -\frac{1}{2}x$?
• Jun 2nd 2008, 08:57 AM
wingless
Quote:

Originally Posted by cmf0106
Can you adjust assume X = 1 and do $\displaystyle 1 - 3/2$ thus equaling $\displaystyle -\frac{1}{2}x$?

No. It could be $\displaystyle -\frac{1}{2}x^5$ as well. Well, you could only use this method in a test..

Anyway,
$\displaystyle x- \frac{3}{2}x = -8\frac{1}{2}$

Factor the x on LHS,
$\displaystyle x\cdot \left ( 1 - \frac{3}{2} \right ) = -8\frac{1}{2}$

$\displaystyle x\cdot \left (- \frac{1}{2} \right ) = -8\frac{1}{2}$

$\displaystyle -\frac{1}{2}x = -8\frac{1}{2}$
• Jun 2nd 2008, 09:03 AM
cmf0106
Thanks for clarifying, that makes perfect sense. However, does LHS mean left hand side of the equation?
• Jun 2nd 2008, 09:06 AM
wingless
Quote:

Originally Posted by cmf0106
Thanks for clarifying, that makes perfect sense. However, does LHS mean left hand side of the equation?

Exactly (Yes)
• Jun 3rd 2008, 08:54 AM
cmf0106
Actually one last question I forgot to ask yesterday the problem reads

$\displaystyle x + 8 = \frac{3}{2}x - \frac{1}{2}$

$\displaystyle x= \frac{3}{2}x -8\frac{1}{2}$

I am not certain how the "$\displaystyle -8\frac{1}{2}$" is created exactly. The RHS reads $\displaystyle \frac{3}{2}x - \frac{1}{2} - 8$ So I assume you can just do (once you subtract 8 from both sides in the first equation displayed) "$\displaystyle -\frac{1}{2} - 8$" which in a calculator = -8.5 or $\displaystyle 8\frac{1}{2}$

Could some one please clarify, thanks.
• Jun 3rd 2008, 09:19 AM
topsquark
Quote:

Originally Posted by cmf0106
Actually one last question I forgot to ask yesterday the problem reads

$\displaystyle x + 8 = \frac{3}{2}x - \frac{1}{2}$

$\displaystyle x= \frac{3}{2}x -8\frac{1}{2}$

I am not certain how the "$\displaystyle -8\frac{1}{2}$" is created exactly. The RHS reads $\displaystyle \frac{3}{2}x - \frac{1}{2} - 8$ So I assume you can just do (once you subtract 8 from both sides in the first equation displayed) "$\displaystyle -\frac{1}{2} - 8$" which in a calculator = -8.5 or $\displaystyle 8\frac{1}{2}$

Could some one please clarify, thanks.

I find the whole $\displaystyle 8 \frac{1}{2}$ notation hazardous to begin with. Unless you are told otherwise by your instructor I'd advise you to write it as an "improper fraction:"
$\displaystyle 8 \frac{1}{2} = 8 + \frac{1}{2} = \frac{17}{2}$