Question

What does “No values of x make the equation true.” Mean?

Answer 1

Answer:

It means that there is no solution to the equation

Step-by-step explanation:

Answer 2

Step-by-step explanation:

There are some equations for which there is no value of x that can make both of them true at once.

Take  $\frac{1}{x+3} +\frac{1}{x-3} =\frac{6}{x^2-9}$  as an example. Let us see what happens when we try to solve for x.

$\frac{1}{x+3} +\frac{1}{x-3} =\frac{6}{x^2-9} \\\\\frac{x-3}{x^2-9} +\frac{x+3}{x^2-9} =\frac{6}{x^2-9} \\\\\frac{2x-6}{x^2-9} =0\\\\\frac{2(x-3)}{(x+3)(x-3)} =0\\\\\frac{2}{x+3} =0\\\\2=0(x+3)\\\\2=0$

As you can see, the end of our "solution" gave us 2=0, which is not true. This means that there are no solutions to this equation. Therefore, there are no values of x to make this equation true.