Write the other side of this equation so that it is true for no
values of .

To create an equation that has no solutions for , we can manipulate the left side of the equation to yield an impossible statement or an equation that results in a contradiction.

Let’s take and simplify it:

Now, to create a scenario with no solutions, we can say that is our manipulated form, but we want an impossible scenario.

Let’s say:

Now rearranging gives:

To ensure there are no solutions, let’s modify this to produce a contradiction. Instead, write:

Now simplifying would get:

This is the contradictory statement since -5 cannot equal 1! Thus, the right side should be for the equation to have no solutions. So, the final equation is: