SOLUTION: If k is a constant and 2x+5=3kx+5 for all values of x, what is the value of k?

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Question 1011030: If k is a constant and 2x+5=3kx+5 for all values of x, what is the value of k?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2B5=3kx%2B5

Subtract 5 from both sides

2x=3kx

Divide both sides by 3x, which can only be
done for non-zero values of x.

2x%2F%283x%29=%283kx%29%2F%283x%29

2%2F3=k

That's no doubt the desired value of k, but we must continue
on to show that it is also true when x=0 and k=2%2F3.

So we investigate to see if it also holds true for x=0:

When we replace k by 2%2F3 in 

2x%2B5=3kx%2B5

we get 

2x%2B5=3%282%2F3%29x%2B5

and when we substitute x=0

2%280%29%2B5=3%282%2F3%29%280%29%2B5

0%2B5=0%2B5

5=5

Now since we have shown that it also holds for x=0, 
it holds for ALL values of x.

[To have a rigorous proof we needed to show that
it also held for x=0]

Edwin