What is an inequality?
an inequality is a math question using these symbols: <, >, ≤, ≥
what do these symbols mean?
< = less than
> = greater than
≤ = less than or equal to
≥ = greater than or equal to
unlike normal math equations inequalities can have infinite answers.
ex: 4>x
x can be 3, 2, 1, 0, -1….
now that we got that out of the way; inequalities can be just like normal math equations!!! (with some exceptions)
ex: 
or 
which means any number that is -5.25 or bigger could be the answer.
to check that’s true we can replace x by 6 to see if we get a true statement.
and as we can see here -1 is in fact smaller than 14 which means we did our work right. we can also check the equal sign to see if we really did the work right by replacing x by -5.25 and seeing if we get an equivalent equation when we solve it.
and as we can see here -8.5 is equivalent to -8.5 which means we did a perfect job on this equation.
Exceptions
there is 1 exception when working with inequalities and that is when multiplying both sides by a negative when you do that you need to flip the symbol for example > turns into < also when you have an equation like 4 < x and you want to make it x > 4 you need to flip the symbol.
How to put inequalities on a number line
To put inequalities on a number line its easy for example if you have -2 < x then you would get
its that easy
but you need to watch out for these symbols: ≤ and ≥
for these symbols you need to do the same thing but instead of leaving an open dot you make a solid dot. If its a solide dot that means that that number and bigger/smaller is the answer is you leave it an ope dot than that means that the answer is bigger/smaller then that number not including that number.
ex: -5 ≤ x
now you might run into stuff to model like this 0 < x ≤ 4 dont worry that just means your going to have to have the answer in-between 0 and 4. To put in on a number line you need to make the line from 0 to 4 without arrows and have them connect at both dots like this.
