what's the value of k

Question

k(10x-5)=2(3+x)-7

 

If the equation above has infinitely many solutions and k is a constant, what's the value of k?

Answer 1

You can distribute & rearrange terms to get   x(10k-2) = 5k -1  or  2x(5k-1) = 5k-1.

 

If k = 1/5, then the left side and the right side are both zero, so it doesn't matter what x is...x can be any Real number.