# Lesson 3.5 - Ashland Independent Schools

```College Algebra: Lesson 3.5 Linear Inequalities in Two Variables
Recall:
1. To graph a line, you must plot two points.
2. When graphing a linear inequality, the boundary line will either be dotted or solid. If the symbol is &lt; or &gt;,
the line will be DOTTED. If it is  or  , the line will be SOLID.
3. After graphing the boundary line, you must shade one side of the line. You substitute one point (not on the
line) into the inequality. If the point makes the inequality TRUE, you shade the side with the point. If it makes
the inequality false, shade the other side.
Examples:
Graph the solution set of the following linear inequality. a. Choose the type of line: solid or dashed. b. Enter
two points on the boundary line. c. Select the region you wish to be shaded.
1. 5(y + 1) &lt; - x
2. 12x + 3  -12 y + 3
Recall:
1. Compound inequalities: &quot;OR&quot; = Union; &quot;AND&quot; = Intersection
2. A system of inequalities is two (or more) inequalities. When graphing an &quot;OR&quot; inequality, the solution is
EVERYTHING that is shaded. When graphing an &quot;AND&quot; inequality, the solution is where the shaded regions
overlap.
3. Absolute value inequalites: ??? # is rewritten as an OR; ??? # is rewritten as an AND
Examples:
Solve the system of two linear inequalities graphically. (Will have you do in three parts.)
1. 2x - 6y &lt; -6 and x  6
2. 4y &lt; -6x or 4y  -4x - 24
3. 4 x  7  29
4. 3x  6 y  21
5. Graph the solution set to the following linear inequality: 9 x  11  25
Convert the inequality into two inequalities in standard form.
Inequalities: ____________
Select the correct graph.
and/or _____________
6. Graph the solution set to the following linear inequality: 2 x  1  12 or 2 y  1  12
```