What do you think it means for a number to be a solution to an equation?
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?
Question 2
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.
A Solution
\(x+1=4\)
\(3+1=4\)
\(4=4 ~ ( \checkmark ) \)
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.
Not A Solution
\(x+1=4\)
\(4+1=4\)
\(5=4 ~ ( \chi ) \)
False Statement
(D3 9A - 9:10A) Intro to Solutions
By Anurag Katyal
