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7.5: Linear Inequalities Objective- To graph linear inequalities and write/use them in real world situations. Vocabulary: 1. Linear Inequality- _____________________________________________________________ _____________________________________________________________________________ 2. Solution of an Inequality- _______________________________________________________ ____________________________________________________________________________ Investigate: Graphing Inequalities 1. Graph y = x + 4 on the coordinate plane. 2. Test 3 points that lie above the line y = x + 4. Substitute the coordinates of the point (x, y) in the inequality y > x + 4. If the results are true statements, mark the points on the graph. 3. Test 3 points that lie below the line y = x + 4. Substitute the coordinates of the point (x, y) in the inequality y > x + 4. If the results are true statements, mark the points on the graph. 4. Critical Thinking: To graph y > x + 4, would you choose points above or below y = x + 4? 5. Determine with out graphing whether you would choose points above or below the graph of y = x – 2 to graph y < x – 2. Notes: Symbol > or < or Line Example 1: Graphing an Inequality a.) y > -2x + 1 b.) y 4/3x - 9 c.) y > x -1 Example 2: Real World Problem Solving Budget- Suppose your budget allows you to spend no more than $24 for decorations for a party. Streamers cost $2 for a roll and table cloths cost $6 each. Graph the inequality that represents the situation.