My teacher is a bad explainer so I need someone else who can explain it to me again.
I want to know what it means for a set of numbers to be a solution for an equation or inequality.
A thorough explanation if possible please~
My teacher is a bad explainer so I need someone else who can explain it to me again.
I want to know what it means for a set of numbers to be a solution for an equation or inequality.
A thorough explanation if possible please~
If you have two or more possible solutions to an equation, then the full solution is the set of all possible solutions.
A simple example is the quadratic equation $\displaystyle x^2 - 5x + 6=0$.
When factorised, this gives $\displaystyle (x-3)(x-2)=0$
and so by the null factor law
$\displaystyle x - 3 = 0$ or $\displaystyle x - 2 = 0$
and so $\displaystyle x = 3$ or $\displaystyle x = 2$.
So the solution set is $\displaystyle x = \{2, 3\}$.
Does that make sense?
There are two possible x values that make the above equation true, x=2, and x=3.
A set is an abstract collection of objects - could be the set of all bananas, the set of all elephants, or more commonly in mathematics, a set of numbers.
For example the set of all even numbers is written within curly parenthesis like so: $\displaystyle \mathbb{Z}_{Even}=\{2,4,6,8,\cdots\}=\{2n:n\in\mat hbb{Z}\}$
In this case we have the set of all solutions to the equation: {2,3}