Alg2 lesson 2-7
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The document provides examples of solving inequalities and determining whether boundary lines are included in solution sets. Example 1 shows testing points to determine which side of a boundary line satisfies an inequality. Example 2 involves writing and graphing an inequality about the number of students and chaperones that can ride on a bus being less than or equal to 60. Example 3 tests a point to shade the region satisfying the original inequality.
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Alg2 lesson 2-7
- 1. Example 7-1a Determine the location of the boundary line x – 2y = 4 Is the boundary line included in the solution set? ≥ or ≤ includes the line SOLID LINE > or < does not include the line BROKEN LINE Graph
- 2. Example 7-1b Test (0 , 0) . Shade the region that contains (0 , 0) . 3) Pick a test point to find the side of the line that contains points which make the inequality true. x Graph true
- 3. Example 7-1c 2x + 5y = 10 x-intercept: 2x + 5(0) = 10 2x = 10 x = 5 (5, 0) y-intercept: 2(0) + 5y = 10 5y = 10 y = 2 (0, 2) Solid or broken line? BROKEN Graph
- 4. Example 7-1c Test any point that is not on the line Test (0, 0) 2(0) + 5(0) > 10 0 + 0 > 10 0 > 10 FALSE Shade the true side Graph
- 5. Example 7-2g Class Trip Two social studies classes are going on a field trip. The teachers have asked for parent volunteers to also go on the trip as chaperones. However, there is only enough seating for 60 people on the bus. a. Write an inequality to describe the number of students and chaperones that can ride on the bus. Students + chaperones ≤ 60 Answer:
- 6. Example 7-2h b. Graph the inequality. c. Can 45 students and 10 chaperones go on the trip? Answer: yes x Answer:
- 7. Example 7-3a Test (0 , 0) . Shade the region that contains (0 , 0) . x Graph Original inequality true