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Mastering Inequalities with Number Lines - Graphing and Solving Techniques

Learn to write and graph inequalities on a number line accurately. Practice solving and graphing equations for a solid understanding. Understand the symbols and their meanings for effective problem-solving.

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Mastering Inequalities with Number Lines - Graphing and Solving Techniques

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  1. Name __________________ Section 5.3 Inequalities Objectives: Write Inequalities Graph inequalities on a number line

  2. Review: • Solve and graph each equation on a number line.

  3. Inequalities:

  4. Steps: • Solve the inequality the same way you would solve an equation. • Check the solution by plugging in a number greater than the result and a number less than the result. • Mark the result on the number line with either a solid dot or an open circle. • Shade either to the left or the right.

  5. Write Inequalities An inequality is a mathematical sentence that compare quantities that are not equal. Inequalities contain the symbols <, >, <, or >

  6. Examples Write an inequality for each sentence 1. The DVD costs more than $15 2. The speed limit is less than or equal to 35 miles per hour.

  7. Practice 3. A student must have at least 10 hours of instructor assisted driving time to pass the course. Write an inequality to describe this situation. 4. You must be at least 18 years old to vote. Write an inequality to describe this situation.

  8. Notes Inequalities with variables are open sentences. When the variable in an open sentence is replaced with a number, the inequality may be true or false.

  9. Examples For the given value, state whether each inequality is true or false. 1. 2t + 8 > 7; t=1 2. p – 42 < -2; p=40

  10. Graph Inequalities Inequalities can be graphed on a number line. The graph helps you visualize the values that make the inequality true.

  11. Open and Closed Dots When graphing inequalities, an open dot is used when the value should not be included in the solution, as with > and < inequalities. A closed dot indicates the value is included in the solution, as with < and > inequalities.

  12. Examples Graph each inequality on a number line. 1. a > 6 2. x > -2

  13. Problem Solving Write an inequality for each sentence. 1. The elevators in an office building have been approved for a maximum load of 3600 pounds. 2.Children under the age of 2 fly for free.

  14. Essential Question Explain when you would use an open circle and a closed circle when graphing inequalities. ____________________________________________________________________________________________________________________________________

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