Question 341919
{{{(2x)/5 - x/3 = 5}}}
The key is that if you multiply both sides of the equation by
the same number, the equation does not change
The question then is:
What number do you multiply both sides by?
Let me make up my own problem to show you:
{{{1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/x = 5}}}
You must multiply BOTH sides by a number that can be
divided by 2,3,4,5,6, and x without any remainder
I'll takes a guess- how about 30?
Sorry, 30/4 = 7 and 1/2 remainder
How about 60?
Bingo!
60/2 = 30
60/3 = 20
60/4 = 15
60/5 = 12
60/6 = 10
But what do I do with the x?
How do I know if x goes into 60 with no remainder?
The answer is to multiply 60 by x, and then I know
60x/x = 60 hence, no remainder
Now I'll do the work:
{{{60x*(1/2) + 60x*(1/3) + 60x*(1/4) + 60x*(1/5) + 60x*(1/6) + 60x*(1/x) = 60x*5}}}
{{{30x + 20x + 15x + 12x + 10x + 60 = 120x}}}
{{{87x + 60 = 120x}}}
{{{33x = 60}}}
{{{x = 60/33}}}
The answer is not important, but the method is.