Question

How can you tell when a equation in one variable has infinitely many solutions or no solution

Answer 1

Say you have:

`-4x-2=-2-4x`

We have to add 2 on both sides.

`-4x-2+2=-2-4x+2\\-4x=-4x+0`

Now, we have to add 4x.

`-4x+4x=-4x+4x+0\\0=0`

Our variable disappeared but we still have an equality, 0 is equal to 0. Therefore, we say it has infinite solutions.

Answer 2

The equation simplifies to the point that it no longer contains a variable, but expresses a true equation.

Explanation: