4(80+n)=(3k)nspace, 4, left parenthesis, 80, plus, n, right parenthesis, equals, left parenthesis, 3, k, right parenthesis, n in the equation above, kkk is a constant. for what value of kkk are there no solutions to the equation?

We need to find the value of k at which the equation 4(80+n)=(3k)n has no solution.
Let's solve the above equation for n. So,

By using the distributing property.

Subtract 4n from each sides.

Take out n as a common factor
Divide each sides by 3k-4.

So,
Denominator of a rational equation cannot be 0 because if it will be 0 then the equation will be undefined and there will be no solution.
Here the denominator is 3k-4. Let's set up 3k-4=0 to get the answer. So,





So,
So, for there will be no solution.