# How do I solve this?

#### Johninbkk71

A little stuck on this. I eventually got the
answer by working through what x could
be, but it took a long time. So what's the quick way?
Thanks

X over 9 - X - 2 over 3 = 4

#### v8archie

Math Team
\begin{align*}
&&\frac{x}{9} - x - \frac{2}{3} &= 4 \\
&\text{Multiply by $9$ to remove quotients} & x - 9x -6 &= 36 \\
&\text{Collect similar terms} & -8x &= 42 \\
&\text{Divide by $-8$} & \boxed{x = \frac{-21}{4}} \\
\end{align*}
\begin{align*}
& & \frac{x}{9} - \frac{x - 2}{3} &= 4 \\
&\text{Multiply by $9$ to remove quotients} & x - 3(x - 2) &= 36 \\
&\text{Expand the brackets} & x - 3x + 6 &= 36 \\
&\text{Collect similar terms} & -2x &= 30 \\
&\text{Divide by $-2$} & \boxed{x = -15}
\end{align*}

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#### Johninbkk71

Thanks. If you have time, how would you solve this?
I've used the same problem with a small change.

9 over x - x+2 over 3 = 4

Last edited by a moderator:

#### v8archie

Math Team
I'd do it in exactly the same way.

\begin{align*}
& & \frac{x}{9} - \frac{x + 2}{3} &= 4 \\
&\text{Multiply by $9$ to remove quotients} & x - 3(x + 2) &= 36 \\
&\text{Expand the brackets} & x - 3x - 6 &= 36 \\
&\text{Collect similar terms} & -2x &= 42 \\
&\text{Divide by $-2$} & \boxed{x = -21}
\end{align*}

#### Johninbkk71

Thanks. Got it now.

#### NinjaX3

Excellent algebra skills

Explanation was great and made sense.

A couple of links that were a big help and refresher for me.