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

Answer:

Given equation: mx =5           ......[1]

To find for which values of m does the given equation have a single solution.

Divide equation [1] both sides by x,

$\frac{mx}{x} = \frac{5}{x}$

Simplify:

$m = \frac{5}{x}$

The value of m have a single solution for all real values of x except x≠0.

No solution states that there is no answer to the equation

Infinite solutions  states that any value for the variable would make the equation true.

we can write equation [1] as;

$x= \frac{5}{m}$

For the value of m = 0 , the given equation does not have solutions.

For any constant parameter m ,

$x=\frac{5}{m}$, the given equation does not have any infinite number of solutions.