What is an inequality?
An inequality compares two different values using symbols that show one side is either less than or greater than the other side. With inequalities you never use an equal sign because the two sides are not supposed to be equal. There is no right answer as the variable could be whatever you chose, but it just has to make the statement is true.
What the symbols mean (>, <, ≤, ≥):
With inequalities there are four different symbols that you can use. If the number that is on the left is bigger than the number on the right then you would use “>”. If the number on the left is smaller then the number on the right then you would use “<“. The new symbols that we learned represent that the number is either greater/less than or equal to the other number. “≤, ≥”. The line on the bottom is representing the equal sign.
How to solve and dividing by a negative:
When you are solving an inequality you are doing the same thing that you would be doing if you are solving an equation. You still have to follow the legal moves, whatever you do to one side you have to do to the other and you still have to follow the BFSD rule (Brackets, fractions, sort, divide). The goal is still to get the variable to one side of the symbol with a value on the other side so you can solve for the variable.
At the very end of you solving you have to divide to isolate your variable and get it by itself. When the number you are dividing by is positive you just divide both sides and it is done, but if it is negative and you divide by a negative then your end statement will not be true. When dividing a negative you have to flip the symbol. If the symbol was “<” then it would change to “>”.
Graphing inequalities:
Graphing inequalities are different than how you would normally graph numbers. When you are graphing inequalities there are many numbers that are possible answers to the question. There are two different circles that you use to show what the graphing is trying to demonstrate. If you draw a closed dot then it is representing the greater/less than or equal to signs (≤, ≥), but if it is an open do it is representing that the number is either greater or less than (>, <).
How to check solutions:
To check your solutions there are two possible ways to do it. The first one checks if the statement is true and the second one is if the algebra is correct.
Statement: To check if the statement is true you replace the variable with a number that you think could possibly work and once you replace it you solve the inequality like you would normally, algebraically.
Algebra: When solving it with algebra you replace the variable with the value that was on the other side of the symbol. You would then solve the equation with the substituted variable and when you get the answer both sides should be equal, if they are not then you may have done something wrong and you should check your work.