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May 7th, 2014, 05:42 PM  #1 
Newbie Joined: May 2014 From: Bangkok Posts: 6 Thanks: 0  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 
May 7th, 2014, 06:00 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra 
\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. 
May 7th, 2014, 06:45 PM  #3 
Newbie Joined: May 2014 From: Bangkok Posts: 6 Thanks: 0 
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". 
May 7th, 2014, 06:56 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,690 Thanks: 2669 Math Focus: Mainly analysis and algebra 
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*} 
May 7th, 2014, 07:08 PM  #5 
Newbie Joined: May 2014 From: Bangkok Posts: 6 Thanks: 0 
Thanks. Got it now.

July 13th, 2019, 07:31 PM  #6 
Newbie Joined: Jun 2019 From: New York Posts: 23 Thanks: 0  Excellent algebra skills
Explanation was great and made sense. A couple of links that were a big help and refresher for me. 
July 14th, 2019, 12:46 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 21,028 Thanks: 2259 
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 wellintentioned, 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. 