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Lesson 6-1

Lesson 6-1. Solving Inequalities by Addition and Subtraction. Transparency 1. Click the mouse button or press the Space Bar to display the answers. Transparency 1a. Objectives. Solve linear inequalities by using addition Solve linear inequalities by using subtraction. Vocabulary.

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Lesson 6-1

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  1. Lesson 6-1 Solving Inequalities by Addition and Subtraction

  2. Transparency 1 Click the mouse button or press the Space Bar to display the answers.

  3. Transparency 1a

  4. Objectives • Solve linear inequalities by using addition • Solve linear inequalities by using subtraction

  5. Vocabulary • Defining a variable – letting a variable represent one of the unspecified numbers in the problem • Formula – is an equation that states a rule for the relationship between certain quantities • Set-builder notation - a concise way of writing a solution set. For example, {t l t < 17} represents the set of all numbers t such that t is less than 17

  6. Key Concept xxxxx

  7. Original inequality Add 12 to each side. This means all numbers greater than 77. Example 1 Solve s – 12 > 65. Then check your solution. Check Substitute 77, a number less than 77, and a number greater than 77. Answer: The solution is the set {all numbers greater than 77}.

  8. Original inequality Add 9 to each side. Simplify. Answer: Since is the same as y 21, the solution set is The heavy arrow pointing to the left shows that the inequality includes all the numbers less than 21. The dot at 21 shows that 21 is included in the inequality. Example 2 Solve 12 ≥ y – 9. Then graph it on a number line.

  9. Original inequality Subtract23from each side. Simplify. Answer: The solution set is Example 3 Solve q + 23 < 14. Then graph the solution.

  10. Original inequality Subtract 12n from each side. Simplify. Answer: Since is the same as the solution set is Example 4 Solve 12n – 4 ≤ 13n. Then graph the solution.

  11. Seven timesa number is greaterthan six timesthat number minus two. 7n > 6n – 2 Original inequality Subtract 6n from each side. Simplify. Answer: The solution set is Example 5 Write an inequality for the sentence below. Then solve the inequality. Seven times a number is greater than 6 times that number minus two.

  12. Summary & Homework • Summary: • If any number is added to each side of a true inequality, the resulting inequality is also true • If any number is subtracted to each side of a true inequality, the resulting inequality id true • Homework: • Pg 321 14-44 even

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