SOLUTION: hi can you help me understand how multiplying fractions by LCM simplifies this linear equation ? even though i know how to do it but i dont understand how it works this is a dir

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Question 1082260: hi can you help me understand how multiplying fractions by LCM simplifies this linear equation ?
even though i know how to do it but i dont understand how it works
this is a direct copy from a book
step 1+3x%2F2+=+x%2F5+-+39%2F5
step 2+%2810%293x%2F2+=+%2810%29x%2F5+-+%2810%29+39%2F5
result +15x+=+2x+-+78
+x+=+-6
my main problem with this is that when we multiply all the fractions by 10 it also has effects on the term x so i dont understand why it dosent change the result if you can please explain step by step how it works thanks.

Found 2 solutions by Fombitz, MathTherapy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look at it like this instead.
You're not multiplying by 10 but by 2%2A5 instead.
You're trying to get rid of every denominator in your equation and make for simpler addition and subtraction.
.
.
.

%282%2A5%29%28%283x%29%2F2%29=%282%2A5%29%28x%2F5%29-%282%2A5%29%2839%2F5%29

5%283x%29=%282%29x-2%2A39
15x=2x-78
13x=-78
x=-6

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

hi can you help me understand how multiplying fractions by LCM simplifies this linear equation ?
even though i know how to do it but i dont understand how it works
this is a direct copy from a book
step 1+3x%2F2+=+x%2F5+-+39%2F5
step 2+%2810%293x%2F2+=+%2810%29x%2F5+-+%2810%29+39%2F5
result +15x+=+2x+-+78
+x+=+-6
my main problem with this is that when we multiply all the fractions by 10 it also has effects on the term x so i dont understand why it dosent change the result if you can please explain step by step how it works thanks.
3x%2F2+=+x%2F5+-+39%2F5
10%283x%2F2%29+=+10%28x%2F5%29+-+10%2839%2F5%29 --------- Multiplying EACH TERM by LCD, 10
---- Cancelling denominators with numerators
5(3x) = 2(x) - 2(39)
15x = 2x - 78
15x - 2x = 78
13x = 78
highlight_green%28matrix%281%2C3%2C+x%2C+%22=%22%2C+-+6%29%29