For each of these three equations, determine whether there are any solution(s). If there are solutions, say what they are and show how you found them. If there aren't solutions, explain why not.

(a) x/3+x/4+ x/5 =2x/3 + 2x/4 + 2x/5

(b) y/3+y/4+ y/5 = y/3+ y/4+ y/5+1

(c) z/3+ z/4+ z/5 =z/4+z/5+ z/6+1

Question

For each of these three equations, determine whether there are any solution(s). If there are solutions, say what they are and show how you found them. If there aren't solutions, explain why not. 

(a)  x/3+x/4+ x/5 =2x/3 + 2x/4 + 2x/5 

(b)  y/3+y/4+ y/5 = y/3+ y/4+ y/5+1 

(c) z/3+ z/4+ z/5 =z/4+z/5+ z/6+1

tkhunny · Answer

Didn't we just do this?

You have some arithmetic in front of you.  Have at it.  A little work in Common Denominators, I'd say.

tkhunny · Answer

Can you add x/3 + x/4?

tkhunny · Answer

Of course, you don't actually need to do that.  Just checking.

(a) Factor out 2 from the right hand side.  Anything look cool?
(b) Subtract the three variable-laden terms.  What's left?
(c) Two of the variable terms match up.  Subtract them is see if you can tell where to go.

tkhunny · Answer

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