Question 118193: is there more than one way to solve inequalities, perhaps a shortcut?
can you show me using an example?
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! Solving linear inequalities is   to solving   , except for one detail: you     whenever you multiply or divide the inequality by a  .
Use the addition, subtraction, multiplication, and division properties of inequalities to solve linear inequalities. We always want to get the variable on one side and everything else on the other side by using inverse operations.
some examples:
 …add  to the both sides
 …
 …
Solution are all  values from  to  , where is excluded.
We can write it like this: interval (,)
As you can see from this example, the only difference here is that you have a "  " sign, instead of an " " sign.
Note that the solution to a "less than, but not equal to" inequality is graphed  a  (or else an open dot) at the endpoint.
 ……..move  to the left and  to the right
 ……..
 ……..
Solution are all values from to  , where is included.
We can write it like this: interval (,]
Note that the solution to a "less than or equal to" inequality is graphed with a bracket (or else a closed dot) at the endpoint.
 ......divide both sides by (remember, you flip the sign )
Graphing Inequalities
When is less than a constant (for example  ), you darken in the part of the number line that is   of the  .
Also, because there is    , we are   where is equal to the constant.
That means we are not including the  . One way to notate that is to use an open hole at that point.
When is greater than a constant (for example  ), you darken in the part of the number line that is to the right of the constant.
Also, because there is , we are where is equal to the constant.
That means we are not including the endpoint. One way to notate that is to use an open hole at that point.
When is less than or equal to a constant (for example  ), you darken in the part of the number line that is to the left of the constant.
Also, because there is an equal line, we are where is equal to the constant. That means we are  the endpoint. One way to notate that is to use an closed hole at that point.
When is greater than or equal to a constant (for example  ), you darken in the part of the number line that is to the right of the constant.
Also, because there is an equal line, we are where is equal to the constant. That means we are the endpoint. One way to notate that is to use an closed hole at that point.
Properties for Inequalities:
Addition/Subtraction Property for Inequalities
If  , then 
If , then 
Multiplication/Division Properties for Inequalities
when multiplying/dividing by a positive value
If AND  is positive, then 
If AND is positive, then 
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