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-37/24= 1/2n+1/3

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2 Answers

Hi Ellie;
-37/24= (1/2)n+1/3
Fractions are so annoying and confusing.  Let's get rid of these...
The denominators are 24, 2 and 3.
Let's multiply both sides by 24...
(24)(-37/24)=(24)[(1/2)n+1/3]
-37=12n+8
Let's subtract 8 from both sides...
-8-37=12n+8-8
-45=12n
Let's divide both sides by 12...
-45/12=(12n)/12
-45/12=n
-15/4=n
Let's check our results...
-37/24= (1/2)n+1/3
-37/24= [(1/2)(-15/4)]+1/3
-37/24=(-15/8)+1/3
Let's note the fact that (1/3)(8/8)=8/24.
Let's note the fact that (-15/8)(3/3)=-45/24
-37/24=(-45/24)+(8/24)
The denominators are identical.  These cancel...
-37=-45+8
-37=-37
I'm assuming you mean -37/24=(1/2)n+(1/3)
subtract 1/3 from both sides
(-37/24)-(1/3)=(1/2)n+(1/3)-(1/3)
(-37/24)-(8/24)=(1/2)n
(-45/24)=(1/2)n
multiply both sides by 2
(2)(-45/24)=(2)(1/2)n
-90/24=n
simplify
-45/12=n, or
-3  9/12=n
-3  3/4=n