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Inequalities and Solutions: Learning Graphs

Explore solutions of inequalities, learn to write and graph them, and understand key vocabulary. Practice evaluating solutions and graphing inequalities correctly with examples.

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Inequalities and Solutions: Learning Graphs

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  1. Wednesday, October 27 Objective: Students will identify solutions of inequalities and write inequalities. • Today’s Agenda: • No homework due today. • Fill in planner with today’s assignment (Practice 3-1) • Bell work Make a stem and leaf plot and find the mean, median, mode, and range of your Chapter 2 test scores: 103, 94, 96, 81, 73, 92, 74, 101, 60, 98, 83, 80, 81, 82, 99

  2. Inequalities and their Graphs What is an Inequality? An inequality is a statement that two expressions are not equal 2 3 4 5 6 7 8

  3. Vocabulary solution • A _______________________ of an inequality is any number that makes the inequality true.

  4. Identifying Solutions of an Inequality • Are each of these a solution to x>5? • 7 • -1 • 0.5 Yes; 7>5 is true No; -1>5 is not true No; 0.5 > 5 is not true 2 3 4 5 6 7 8

  5. Identifying Solutions of an Inequality by Evaluating • Is each number a solution of the inequality? • 3 Substitute the value for x Simplify Compare 3 does not make the equation true, so 3 is not a solution.

  6. Identifying Solutions of an Inequality by Evaluating Is each number a solution of the inequality? b) -4 Substitute the value for x Simplify Compare -4 does not make the equation true, so -4 is a solution.

  7. Inequalities and their Graphs Terms you see and need to know to graph inequalities correctly < less than Notice open circles > greater than

  8. Inequalities and their Graphs Terms you see and need to know to graph inequalities correctly ≤ less than or equal to ≥ greater than or equal to Notice colored in circles

  9. Inequalities and their Graphs Example 1 Notice: when variable is on left side, sign shows direction of solution 3

  10. Inequalities and their Graphs Example 2 Notice: when variable is on left side, sign shows direction of solution 7

  11. Inequalities and their Graphs Example 3 Notice: when variable is on left side, sign shows direction of solution Color in circle -2

  12. Inequalities and their Graphs Example 4 Notice: when variable is on left side, sign shows direction of solution 8 Color in circle

  13. Practice

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