# Math Help - Simplifying Linear Equations

1. ## Simplifying Linear Equations

This is some steps into the equation

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

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

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

2. Originally Posted by cmf0106
Can you adjust assume X = 1 and do $1 - 3/2$ thus equaling $-\frac{1}{2}x$?
No. It could be $-\frac{1}{2}x^5$ as well. Well, you could only use this method in a test..

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

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

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

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

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

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

5. Actually one last question I forgot to ask yesterday the problem reads

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

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

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

Could some one please clarify, thanks.

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

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

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

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

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