SOLUTION: "Determine whether each statement is TRUE or FALSE. If FALSE, show or explain how you know." (2k)/(2x+h)=(k)/(x+h) What is the best way to do these problems? To get my answer o

Algebra.Com
Question 1043006: "Determine whether each statement is TRUE or FALSE. If FALSE, show or explain how you know."
(2k)/(2x+h)=(k)/(x+h)
What is the best way to do these problems? To get my answer of false, I plugged in "1" for each variable, is this a valid method?

Found 3 solutions by rothauserc, jim_thompson5910, Edwin McCravy:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
(2k) / (2x+h) = (k) / (x+h)
:
cross multiply the fractions
:
k(2x+h) = 2k(x+h)
:
2kx + kh = 2kx + 2kh
:
kh = 2kh
:
**********************
The statement is false
**********************
:

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Yes you can plug in any set of values for x, k and h (as long as the denominator isn't zero). So I'm going to plug in x = 0, h = 1 and k = 2.














Which is a false equation


So the original equation is false.

Edit: if h = 0 and x was nonzero, then the equation would be true. However, the equation is not true in general. So the answer is still false.

Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Well, in this case substituting k = x = h = 1
did happen to work, since
 






which is false.  So k=x=h=1 does produce
a counter-example.

However if the problem had been instead



and you substituted k = x = h = 1 







That would have been true, not false.  So you would
in that case need to use another number besides 1,
say 2, in order to get a counter-example.

For instance if you substituted k = x = h = 2 in



you get





which is false.

My point is that you may have to substitute other
values for x, h, and k besides 1 in order to find a 
counter-example.  Never assume that if you get a true 
equation, that the given equation is necessarily true.

In fact in some cases you cannot use the same value
for all the variables.  Take



If you use the same values for all three variables
you will never get a counter-example.

You'd have to use something like k=1, h=2, and k=3
to get a counter-example.

Edwin





RELATED QUESTIONS

Determine whether the following statement is true or false: The maximum value of the... (answered by Alan3354)
Determine whether the statement is true or false. If it is false, explain why or give an... (answered by ikleyn)
tell whether each statement is true or false: if two lines intersect, then the adjacent... (answered by richwmiller)
Determine whether the following is a statement. If it is, then also classify the... (answered by lynnlo)
Determine whether the statement is true, false, or sometimes true. If x is positive and (answered by edjones)
Determine whether each statement is true or false 3 logb 3√a = logb a (answered by jsmallt9)
Tell whether each statment is true or false. Then write the converse and tell whether it... (answered by engchunh)
Determine whether each statement is true or false. If it is false, provide a... (answered by stanbon)
Determine if the conditional statement is true or false given the following: p is... (answered by solver91311,htmentor)