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May 7th, 2014, 05:42 PM   #1
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How do I solve this?

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
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May 7th, 2014, 06:00 PM   #2
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\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*}

Last edited by v8archie; May 7th, 2014 at 06:06 PM.
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May 7th, 2014, 06:45 PM   #3
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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 skipjack; July 13th, 2019 at 11:37 PM. Reason: to add "3" after "over".
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May 7th, 2014, 06:56 PM   #4
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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*}
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May 7th, 2014, 07:08 PM   #5
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Thanks. Got it now.
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July 13th, 2019, 07:31 PM   #6
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Excellent algebra skills

Explanation was great and made sense.

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

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July 14th, 2019, 12:46 AM   #7
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Or turn on your calculator, then enter 24 × 21 =

After solving the algebra problem, he insists on checking the answer, but he doesn't mention checking your answer in the first video after doing the multiplication problems.

This teacher seems well-intentioned, but he hasn't thought things through and hasn't linked his videos into an overall course. Also, saying "blow your mind" several times (or just once for that matter) is inappropriate for young children.
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