SOLUTION: If k is a constant and 6x-7=-4(k-w)+2x+1, what value of k guarantees the equation has infinitely many solutions? Thanks

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Question 1143961: If k is a constant and 6x-7=-4(k-w)+2x+1, what value of k guarantees the equation has infinitely many solutions?
Thanks
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Was the "w" a typo and supposed to be "x"?

6x-7=-4%28k-w%29%2B2x%2B1

It must be identically true when x = any number.  
So it must be true when x=0. So we substitute x=0

6%2A0-7=-4%28k-w%29%2B2%2A0%2B1

-7=-4%28k-w%29%2B1

-7=-4k%2B4w%2B1

4k-4w=8, divide through by 4

k-w=2

It must also be true when x=1. So we substitute x=1

6%2A1-7=-4%28k-w%29%2B2%2A1%2B1

6-7=-4%28k-w%29%2B2%2B1

-1=-4k%2B4w%2B3

4k-4w=4, divide through by 4

k-w=1

So we have the system

system%28k-w=2%2Ck-w=1%29

This is an inconsistent system, so there is no solution.  That is,
if you copied it correctly and the "w" is correct.  There would be
a solution, however, if "w" was supposed to be "x".

Edwin