# Linear Equations, Fractions

• Jul 9th 2009, 06:48 PM
allyourbass2212
Linear Equations, Fractions
How would I work this problem out if I did not want to cross multiply?

$\frac{18-5x}{3x+2}=\frac{7}{3}$

• Jul 9th 2009, 07:14 PM
Kasper
Quote:

Originally Posted by allyourbass2212
How would I work this problem out if I did not want to cross multiply?

$\frac{18-5x}{3x+2}=\frac{7}{3}$

I don't know why you would want to do it that way?

Multiply both sides by $3x+2$ and $3$ and you get rid of both denominators and it becomes simple algebra to solve for x.
• Jul 9th 2009, 07:34 PM
Shyam
Quote:

Originally Posted by allyourbass2212
How would I work this problem out if I did not want to cross multiply?

$\frac{18-5x}{3x+2}=\frac{7}{3}$

${\text{Cross - Multiply,}} \hfill \\
$

$\frac{{18 - 5x}}
{{3x + 2}}=\frac{7}
{3} \hfill$

$3(18-5x)=7(3x+2)$
• Jul 9th 2009, 07:47 PM
Kasper
Is this what your trying to do with the LCD?

$\frac{18-5x}{3x+2}=\frac{7}{3}$

$\frac{18-5x}{3x+2}-\frac{7}{3}=0$

$
\frac{3(18-5x)-7(3x+2)}{3(3x+2)}=0
$

Because this still gives you

$3(18-5x)-7(3x+2)=0$

Which is the same as cross multiplying and dividing which gives

$
3(18-5x)=7(3x+2)
$

So you could do it that way, but it's much more work.