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September 6th, 2016, 11:44 PM  #1 
Newbie Joined: Sep 2016 From: alaska Posts: 16 Thanks: 0  Question about a rational equation
I don't even know where to start. I multiplied everything by the LCM and subtracted hoping that it would get me somewhere, but that's about as far as I got. My program is asking for an exact number (no fractions). How would I go about solving for x? ( x+8 )/( 9 ) − ( x−1 )/( 2 ) = 8 Last edited by MBI; September 6th, 2016 at 11:55 PM. 
September 7th, 2016, 12:21 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
$\displaystyle \begin{align*} \frac{x+8}{9}  \frac{x1}{2} &= 8\\ 2(x+8)  9(x1) &= 18 \times 8\\ 2x + 16  9x + 9 &= 144\\ 119 &= 7x\\ x &= 17 \end{align*}$ 
September 7th, 2016, 12:42 AM  #3 
Newbie Joined: Sep 2016 From: alaska Posts: 16 Thanks: 0  I wasn't aware that you should find a LCM for the second part of the equation as well. That's pretty cool thank you.
Last edited by skipjack; October 22nd, 2016 at 03:24 AM. 
September 7th, 2016, 01:56 AM  #4  
Member Joined: Aug 2016 From: Used to be Earth Posts: 64 Thanks: 14  Quote:
But if you want to get rid of the common denominator in the lefthand side, you indeed then have to multiply the righthand side by the fraction $\displaystyle \frac{\text{denominator}}{\text{denominator}}$ (because by definition, anything divided by itself = 1), so this is just like multiplying the right hand side by 1, which doesn't change its result. After doing so, every term in your equation will have the same denominator, and this allows you to simply get rid of it. Hoping this isn't too confusing. Last edited by skipjack; October 22nd, 2016 at 03:36 AM.  
September 7th, 2016, 03:52 AM  #5  
Newbie Joined: Sep 2016 From: alaska Posts: 16 Thanks: 0  Quote:
Last edited by skipjack; October 22nd, 2016 at 03:36 AM.  
September 7th, 2016, 06:31 AM  #6  
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  Quote:
Note: To be good form, the right side of the equation of the second equation as shown above should not be used for two reasons: 1) The "X" looks similar to the x variable, and this is an algebra problem, whereas it would be expected to see that sometimes in an arithmetic problem. 2) It is inconsistent with the rest of the equation. Parentheses should have been continued across for the equation to show multiplication. $\displaystyle \frac{x+8}{9}  \frac{x1}{2} = 8\\$ $\displaystyle 2(x+8)  9(x1) = 18(8) $  
October 21st, 2016, 11:34 PM  #7 
Member Joined: Sep 2016 From: India Posts: 88 Thanks: 30 
$\dfrac{x+8}{9}\dfrac{x1}{2}=8$ $\dfrac{2(x+8 )9(x1)}{18}=8$ $2(x+8 )9(x1)=8\times 18$ $2x+16−9x+9=144$ $2x9x=144169$ $7x=119$ $x=17$ Last edited by deesuwalka; October 21st, 2016 at 11:44 PM. 
October 22nd, 2016, 08:21 AM  #8 
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  Note: To be good form, the right side of the equation of the second equation as shown above should not be used for two reasons: 1) The "X" looks similar to the x variable, and this is an algebra problem, whereas it would be expected to see that sometimes in an arithmetic problem. 2) It is inconsistent with the rest of the equation. Parentheses should have been continued across for the equation to show multiplication. $\dfrac{2(x+8) \  \ 9(x1)}{18} \ = \ 8$ $2(x+8) \  \ 9(x1) \ = \ 8(18)$ 

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