Linear+Inequalities

__**LINEAR INEQUALITIES**__

 **ex.1**  5x - 7 **≥** 3  5x **≥** 3 + 7  5x **≥** 10  **x ≥ 2**

 **ex.2**  -3x + 8 **>** 2  -3x **>** 2 - 8  -3x **>** -6  **x < 2 * When dividing by a negative (-), inequality sign must be switched **

 **ex.3 Double Inequalities**  -5 **≤** 2x+7 **≤** 1  -5 -7 **≤** 2x **≤** 1 -7 // * subtract 7 //  -12 **≤** 2x **≤** -6 // * divide by 2 // <span style="font-family: 'Comic Sans MS',cursive;"> ** -6 ≤ x ≤ -3** *** The same operation is applied to all parts**

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;"> **ex.4** <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;"> 1 **≤** 7 - 3x **≤** 16 <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;"> 1-7 **≤** -3x **≤** 16-7 // * subtract 7 // <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;"> -6 **≤** -3x **≤** 9 // * divide by -3 // <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;"> 2 **≥** x **≥ -3** // * switch inequality sign // <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;"> -3 **≤** x **≤** 2

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;"> **Types of Notations**

<span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;"> -3 **≤** x **≤** 2 <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;"> { -3, 2 } ; (9, 78) ** * {Curly brackets mean # is included} ; (parentheses means # is excluded)** **
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">**Set**
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">**Interval**
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 110%;">**Graphical * Shaded circle means # is included ; hollow circle means # is excluded** **
 * <span style="font-family: 'Comic Sans MS',cursive; font-size: 14px; line-height: 21px;">[[image:http://www.mathamazement.com/images/Pre-Calculus/P_Prerequisites/P11_linear-inequalities/graph-of-solution-to-example-3.JPG width="473" height="57" align="left" caption="graph of interval [-1,3)"]]