What is an inequality?

An inequality is 2 numbers in an equation separated by up to 6 different signs the first sign is less than, the second sign is greater than, the third sign is less than or equal to, the fourth one is greater than or equal to, and the last two are equal to and, not equal to. Lets say that the equation is x < 11. That would mean that x could be anything less than 11. So it could be 10, 9, 8, 7, 6, 5, 4, 3, 2 ,1 ,0, and anything into the negatives as well.

What do the symbols mean?

with greater than and less then ( >, < ) the way that the symbol is pointing always points towards the smaller number. An example for that would be 7 > 6 because 7 is greater than 6. The next is equal to or less than, and equal to or equal than. That works the exact same except for the number could be the same or anything greater or less. If the questions was x is less than or equal to 7 then the answer would be 7 and anything below. The last two are equal to and, not equal to. Equal to is what you would do for the kindergarten classes like 1 + 1 = 2 because it is a true statement. The other one is not equal to which is the equals sign with a line through it and it would be the exact opposite of the normal equals. for example 1 + 1 ≠ 3 because 1 + 1 does not equal 3.

How to solve an inequality?

You solve an inequality basically the exact way that you would have done a linear equation. the number 1 strategy to solving these is using legal moves. that means that whatever you do to one side of the equation, you have to do the exact same thing to the other side. The whole goal is to end up where you have isolated the variable on one side and the number on the other.  An example question will be, 2x -5   1x + 7. What you would do is start off with a legal move like removing 1x from each side so we are left with x – 5   +7. The next step would be to add 5 so it zero pairs the -5. That will leave you with x   12. That means that x is greater than or equal to 12 so the answer could be  12 and up. However, when you are dividing by a negative you need to flip the greater than/less than sign. Let say the question is -3x < 12, after divided you are left with x < -4, but since it is a negative you flip the sign and your answer becomes x > – 4.

How do we graph inequalities?

When you  graph inequalities you have to use the greater than and less than  signs as a dot with a hollow inside. The hollow dot represents that the equation is not a less than or equal to, or more than or equal to. Because of that when you are graphing it you draw a blank circle of the number that x is greater than or less than. Then according to which one it is you draw a line towards the lesser side or the greater side. When you do it with greater than or equal to, and greater than or less than you do it the same way except you do a circle that isn’t hollow and the same thing with the line. This way means it could also be equal to.

How to check a solution

There is more than one way to check a solution. The equation i picked to test is 2x -5   1x + 7. to get to the answer the first thing i would do is make zero pairs by removing 1x and adding 5. Now you are left with x   12. the way we check the answer is by putting a number that in this case is greater than or equal to 12. If it is a true statement then you know that the answer is correct. Another way is by reversing what you did and trying to get to the question you started with but you can only use legal moves. If you do only legal moves than it will be right. For example x   12, to get back to what we started at we subtract 5. that makes it x -5   7, next we add 1x and it leaves us with the starting question of 2x -5   1x + 7

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