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Algebra 2 Unit 2—Graphing Linear Inequalities Notes Date: __________ An inequality is an expression that uses inequality symbols rather than an equal sign. In these notes, we will review how to graph a single inequality, identify the solution region, and explain what the solution region means. We will then graph a system of inequalities (2 or more), identify the solution region, and explain what the solution region means. *Remember that when you are solving an inequality for a variable, if you multiply or divide by a negative number, that will change the direction of the inequality symbol. 3x 6 2 x 4 Objective: I can graph a single linear inequality. Graph each linear inequality: Ex 1: y 3 x 4 Steps to graphing a linear inequality: 1. Solve for _____, if needed. 2. Graph the line using ____ and ____. 3. If using < or >, use a __________ line. If using or , use a __________ line. 4. If using < or , shade ________ the line. If using > or , shade ________ the line. Ex 2: y 3 x5 5 Not every line we need to graph will be in slope-intercept form. Graph each linear inequality below. Ex 3: Graph x 4 Ex 4: Graph y 2 If you have a vertical line: *shade to the __________ for < or *shade to the __________ for > or If you have a horizontal line: *shade __________ for < or *shade __________ for > or Ex 5: Graph 3x 2 y 10 Ex 6: 5 x 3 y 18 Example 7: Is the point (3, -1) a solution to the inequalities above? Explain why. Ex 3: Ex 4: Ex 5: Ex 6: Objective 2: I can graph a system of linear inequalities. Graphing 2 or more inequalities is exactly the same as graphing a single inequality, except the solution will be the region that is double-shaded. The points in that region are solutions to BOTH inequalities. Graph each system below. Which quadrant(s) would have no solution? 3) 4) Ex 5: Name one point in #3 that IS a solution _____________ Name one point in #3 that is NOT a solution _____________ 6)