Imagine you are trying to unlock a locked door.

A solution is a key that not only fits the lock but actually opens the door as well.
A master key will fit and unlock any door and represent all solutions.
An incorrect key will not fit nor unlock the door, representing no solution.
Extraneous solutions are keys that fit but are missing the groves to turn the tumblers in the lock. We will see these later in the course.

Question 1

What number would you add to 1 to get 4?

What number would you add to 1 to not get 4?

We say $3$ is a solution to $x+1=4$ because if we substitute $3$ in for $x$ in the equation, we can simplify to a true statement.

$x+1=4$

$3+1=4$

$4=4 ~ ( \checkmark )$

True Statement

We say $4$ is not a solution to $x+1=4$ because if we substitute $4$ in for $x$ in the equation, we can simplify to a false statement.

$x+1=4$

$4+1=4$

$5=4 ~ ( \chi )$

False Statement