Solving for L

Wej

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May 13, 2020
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I need to isolate L on one side of this equation. I almost have it but can't quite get there. Can you please help me with the last step (or two)? Probably easy for you guys/gals but I'm surprised I got this far. Thanks in advance!


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Can we please be given the equation which you want to solve L for?


BTW since the reciprocal of 360 is 1/360, when you say that you want to divide both sides by the reciprocal of 360 that means that you want to divide both side by 1/360. Is that what you really meant to say??
 
It looks as if the equation were

[MATH]360\div\frac{M}{\frac{G+H+I+J+K+L}{6}} = DIO(N)[/MATH]​

But then DIO disappears. What does it represent?

In any case, I would simplify the LHS a little before solving; if I'm right, you can rewrite it as

[MATH]360\div\frac{6M}{G+H+I+J+K+L} = 360\cdot\frac{G+H+I+J+K+L} {6M} = \frac{60(G+H+I+J+K+L)} {M}[/MATH]​
 
Sorry, DIO was just the description for N. It should just be =N.
 
Ok, I got this far, now I just need to get "L isolated...

60(G+H+I+J+K+L)=N*M
 
Okay, then your next step is to solve [MATH]\frac{60(G+H+I+J+K+L)} {M} = N[/MATH] for L. Give it a try. Most of the hard stuff is eliminated by what I did in simplifying.
 
You're right. A breeze from there. Thanks for your help Doc!

Move 60 to the other side
G+H+I+J+K+L=(N*M)/60
Move G,H,I,J,K to the other side
L=((N*M)/60)-G-H-I-J-K
 
Something I've often told students is, "Clean the kitchen before you start cooking" (or, "Clean the workshop before you start building"). What I mean is, when you have a complicated equation, simplify each side, before you start moving things around on both sides. It's much easier to keep track of things when there isn't a mess lying around on the counter.

On the other hand, there are times when multiplying both sides by a denominator to eliminate a fraction is safer, because the work with fractions in simplifying would be too error-prone. You have to decide what's best for you. This example is dangerous no matter what you do first!
 
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