Question

For what values of m does the equation mx = 5 have a single solution? can m have a value for which the equation does not have solutions; have infinite number of solutions?

Answer 1

We are given equation : mx =5.

We need to solve the equation for m first.

m is being multiplied with x.

So, we need to get rid m from left side.

The reverse operation of multiplication is division, so we need to divide both sides by m, we get

`(mx )/(m) = (5)/(m)`

x =
`(5)/(m)`.

Please see, we have m in denominator.

So, we can't have 0 in denominator.

For all other each real numbers x would have a single solution.

Therefore, solution for m is : All real numbers except 0.

And for m=0 the equation does not have solutions.

And for m=x/5, we have infinite number of solutions.