What I have learned about math 9 inequalities

What are inequalities? A math statement comparing expressions that may or may not be equivalent.

What is the difference between inequalities and equations?                                                           Equations only have one solution and inequalities can have multiple.

Symbols: You may see these symbols <, >,  \geq\leq

So this is x is less then 4: x<4                                                                                                                      So we know x can be any number lower then 4 such as 3,2,1,0,-1,-2, ect…

So this is x is more then 4: x>4.                                                                                                                         So we know x can be any number greater than 4 such as 5, 6, 7, 8, 9, 10, ect…

If the less then greater then symbol has a line under it (\leq  or \geq) means its less (or more) then or EQUAL to a number:

So this is x is less then or equal to 7:  x \leq7

And this is x is more then or equal to 7:   x \geq7

Graphing inequalities: If you had to graph x>7  You would draw a line  and put seven on it then put an arrow pointing to the right because its any number bigger then seven (Because 7 is less then x). The boundary point when graphing is a dot so in x>7 the 7 would be the boundary point (where you put the dot). If it is this < or > you draw a closed dot, if it is this  \geq or this  \leq it would be a closed dot.

Example:

How to solve- dividing by negatives: When dividing by negatives the symbol flips so if it was < it would become >.

Example:

How to check a solution: There is two ways to check a solution. The first way is to check another number so if your answer was x>5 you would put in any number greater then 5 such as 6 so x would be replaced by six so 6>5 this is a true statement so you know you got the right answer.

Click for the Example: medium (30)-1qna2a3

 

The second way is to replace x is to replace it with the answer so if you get x>5 you would resolve the equation replacing x with 5. So if the original equation was 3x-4\leq11 and you think x\leq5.

You would replace x with 5 example: 3(5)- 4\leq11  change the \leq to an = and solve                                                                                                       15 – 4 = 11                                                                                                                                                                             11 = 11

Click for the Example:  medium (1)-1tftdaw

 

 

 

 

 

 

 

 

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