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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 < or >, 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) < - x 2. 12x + 3 -12 y + 3 Recall: 1. Compound inequalities: "OR" = Union; "AND" = Intersection 2. A system of inequalities is two (or more) inequalities. When graphing an "OR" inequality, the solution is EVERYTHING that is shaded. When graphing an "AND" 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 < -6 and x 6 2. 4y < -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