Chapter+6

= =
 * 6.1**

**Solving Inequalities by Addition and Subtraction**
= = x = 2 ☻ = = x > 2 ☺--> = = x < 2 <--☺ = = x ≥ 2 ☻--> = = x ≤ 2 <--☻ = =

If the variable comes first the arrow points the same way as the arrowhead If the number comes before the variable the arrow points the opposite direction = = = **6.2** =

**Solve linear inequalities by using division.**
= = = If you are dividing or multiplying by a negative number you **__MUST__** switch the sign = = = = **6.3** = === Solve linear inequalities involving more than one operation. === = Solve linear inequalities involving the Distributive Property. = //and// means that there will be a line connecting the two circles //or// means that the arrows are going to be pointing in opposite directions

*Keep everything on one side of the equal sign together, and everything on the other side of the equal sign together. = = = = 3<2x-3<15 3<2x-3 2x-3<15 3(+3)<2x-3 (+3) 2x-3 (+3)<15 (+3) 6<2x 2x<18 33
 * Ex: **

= **6.4** =

**Solving compound inequalities**
= = Compond inequality: = = AND = =
 * [[image:http://www.icoachmath.com/image_md/Inequality1.gif caption="external image Inequality1.gif"]] ||
 * external image Inequality1.gif ||

= = OR = =
 * [[image:http://hotmath.com/hotmath_help/topics/compound-inequalities/compound-inequalities-image1.gif caption="external image compound-inequalities-image1.gif"]] ||
 * external image compound-inequalities-image1.gif ||

= = __ Steps: __ = = 1.) Graph one side = =  2.) Graph other side = = 3.) Find the union = = = = __ Steps: __ = =  Solve each inequality individually and the final solution will be the union of these two solutions = =  1.) Start with the first inequality = = 2.) Subtract # from both sides = =  3.) Combine like terms on the right side = = Have first part of the answer! = = 4.) Start with the second inequality = =  5.) Divide both sides to isolate x = = Have the second part of the answer! = = 6.) Put them together to get the answer!
 * Graphing a compound inequality **
 * Solving a compound inequality **

[] = = **6.5**

**Solve absolute value inequalities.**
= = Absolute Value- how many spaces away from 0 a number is (ex. | 10 | = 10 because it is 10 spaces away from 0) = = **To solve an absolute value inequality you must solve two ways** = = | 2n + 1 | < 9 | | < makes the dumbells | | > makes the arrows point away from each other = = ***An OR problem can never make a dumbell (o-o)** = = = = = = = =
 * 1) **Answer stays the same and so does the inequality sign**
 * 2) **Answer changes to the opposite and so does the inequality sign**
 * the same as, equal to, is... **
 * the same as, equal to, is... **
 * greater than, more than, higher, above... **
 * greater than, more than, higher, above... **
 * less than, smaller, lower, under... **
 * less than, smaller, lower, under... **
 * more than or equal to, could differ, as much as... **
 * more than or equal to, could differ, as much as... **
 * within, less than or equal to, could differ, as little as... **
 * within, less than or equal to, could differ, as little as... **

= **6.6** =

**Graphing Inequalities in Two Variables**
**__Graphing Linear Inequalities__**: The solution set of an inequality in two variables is the set of all ordered pairs that satisfy the inequality. Like a linear equation in two variables, the solution set is graphed on a coordinate plane.

**__Half-Plane__**: the region of the graph of an inequality on one side of a boundary.

**__Boundary__**: a line or curve that separates the coordinate plane into regions.

** ** indicate the use of a dashed line

**__<__ and __>__** indicate the use of a solid line

**__Steps:__** 1. Graph the inequality as if it is an equation of a line. .... a) use the x- and y-intercepts to graph the line //**or**// .... b) use a t-chart to graph the line //**or**// .... c) use the slope-intercept form to graph the line 2. Determine if the line should be a dashed line or a solid line by looking at the original inequality.  3. Determine which half-plane to shade by testing an ordered pair from each side to find the side that is true.