# Thread: Solutions to Equations and Inequalities

1. ## Solutions to Equations and Inequalities

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~

2. Originally Posted by aloha.world
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 $x^2 - 5x + 6=0$.

When factorised, this gives $(x-3)(x-2)=0$

and so by the null factor law

$x - 3 = 0$ or $x - 2 = 0$

and so $x = 3$ or $x = 2$.

So the solution set is $x = \{2, 3\}$.

Does that make sense?

3. Originally Posted by Prove It
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 $x^2 - 5x + 6=0$.

When factorised, this gives $(x-3)(x-2)=0$

and so by the null factor law

$x - 3 = 0$ or $x - 2 = 0$

and so $x = 3$ or $x = 2$.

So the solution set is $x = \{2, 3\}$.

Does that make sense?
It kind of makes sense, but can you explain it in words?
...

4. 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: $\mathbb{Z}_{Even}=\{2,4,6,8,\cdots\}=\{2n:n\in\mat hbb{Z}\}$

In this case we have the set of all solutions to the equation: {2,3}