SOLUTION: Can you please help me with this problem: 20/14=(2-x)/7 Thanks! :)

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Can you please help me with this problem: 20/14=(2-x)/7 Thanks! :)      Log On


   

Question 668201: Can you please help me with this problem: 20/14=(2-x)/7
Thanks! :)
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
%2820%2F14%29+=+%282-x%29%2F7
With fractions, my first inclination is always to GET RID OF THEM! How are we going to do that? Just by looking we can see that multiplying by 14 will eliminate fractions as it is a common multiple of the denominators. To generalize, if we want to get rid of fractions, all we have to do is multiply by the LCM (least common multiple) of the denominators. In this case LCM(7,14) = 14.
14%2820%2F14%29+=+14%2A%28%282-x%29%2F7%29
+20+=+2%2A%282-x%29
+20+=+4+-+2x
+16+=+-2x
+x+=+-8+
If you are not comfortable with this method and have a general understanding of fractions, here's the straight-forward way:
20%2F14+=+%282-x%29%2F7
20%2F14+=+2%2F7+-+x%2F7
20%2F14+-+2%2F7++=+-x%2F7
20%2F14+-+4%2F14+=+-x%2F7
16%2F14+=+-x%2F7
-7%2A%2816%2F14%29+=+-7%2A%28-x%2F7%29
-16%2F2+=+x
x+=+-8