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Wetzel
Math 102
8.2 - Linear Inequalities and Absolute Value Inequalities
**Chapter 2**
Inequality Symbols:
<
>
Graphing on a number line:
Interval Notation:
less than
greater than
 less than or equal to
 greater than or equal to
1.) Number line with significant numbers
2.) Open or Closed circle
3.) Arrow to the left or right
1.) Beginning Value, Ending Value
2.)  and - 
3.) ( ) or [ ]
Linear Inequality: (One Variable)
To Solve:
1.) Solve the inequality as if it were an equation
**2.) If you mult. or divide by a negative, “flip” the inequality sign
Compound Inequalities ( “And” Inequalites)
*Solve for the variable in the middle
“Or” Inequalities
*Solve both inequalites. Solutions will be in one or the other.
Examples: Solve in Interval Notation and Graph.
1.) 2 x  5( x  3)  x  9
3.)
x  4  7 or x  8  1
2.)
 8  3x  7  28
Absolute Value Inequality:
To Solve:
1.) Isolate the Abs. Value on the left side
2.) if < or  ,
Rewrite as a compound inequality
If > or  ,
Rewrite as an “Or” inequality
3.) Solve the remaining inequalities
Example: Solve.
4.)
x  4 1
5.)
4 3x  5  16
6.)
8 x  5
7.)
2 2 x  10  19  11