SOLUTION: Can someone please help me with this problem? 1 1/5 + 8 3/14 x = 1 1/30

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Question 540377: Can someone please help me with this problem?
1 1/5 + 8 3/14 x = 1 1/30
Found 2 solutions by mananth, KMST:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
1+%281%2F5%29+%2B+8+%283%2F14%29+x+=+1+%281%2F30%29
Convert all the terms to mixed fractions

%286%2F5%29%2B%28115%2F14%29x+=+%2831%2F30%29

%28115%2F14%29x+=+%2831%2F30%29-%286%2F5%29
On the right side LCD= 30
%28115%2F14%29x+=+%2831-36%29%2F5%29
%28115%2F14%29x+=+%28-1%2F6%29

%28115%2F14%29x+=+-1%2F6
6*115x= -14
x=-14/115*6
x=-0.02
in fraction
x=-7/345








Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
1%261%2F5+%2B+8%263%2F14+x+=+1%261%2F30?
Mixed numbers are usually bad news in algebra. We like to transform them into improper fractions right away. An then we don't like fraction very much, so we tend to multiply everything by a common multiple of the denominators to eliminate those pesky denominators.
In this case, maybe we could use those mixed numbers for a little while. I'll write the equation as
%281%2B1%2F5%29+%2B+8%263%2F14+x+=+1%2B1%2F30
Then I'll subtract 1+1/5 from both sides
8%263%2F14+x+=+1%2B1%2F30-%281%2B1%2F5%29 ---> 8%263%2F14+x+=+1%2B1%2F30-1-1%2F5%29 --> 8%263%2F14+x+=+1%2F30-1%2F5
And calculating on the right hand side
8%263%2F14+x+=+1%2F30-6%2F30 --> 8%263%2F14+x+=+-5%2F30 --> 8%263%2F14+x+=+-1%2F6
It turn out to simplify nicely. Now we have to convert mixed number 8%263%2F14
into an improper fraction.
8%263%2F14=8%2B3%2F14=112%2F14%2B3%2F14=115%2F14
So our equation is
115%2F14+x+=+-1%2F6 and dividing both sides by 115/14 we get
+x+=+%28-1%2F6%29%2F%28115%2F14%29 and calculating the right hand side
+x+=+%28-1%2F6%29%2A%2814%2F115%29 --> +x=+-%287%29%2F%283%2A115%29 --> +x=+-7%2F345