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Graphing Inequalities EXAMPLE 1 InequalityGraphVerbal Phrase a. y < 7 b. q 3 c. x > –5 d. h 2 1 2 All numbers less than 7 All numbers less than or equal to 3 All numbers greater than – 5 All numbers greater than or equal to 2 1 2

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Solving Inequalities EXAMPLE 2 Solve the inequality. Then graph its solution. x – 5 + 5 < 8 + 5 x < 13 Original inequality Add 5 to each side. Simplify. x – 5 < 8 a. x – 5 < 8

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Solving Inequalities EXAMPLE 2 y – 7 –10 y – 7 + 7 – 10 + 7 y –3 Original inequality Add 7 to each side. Simplify. b. y – 7 –10

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Solving Inequalities EXAMPLE 2 8 + m > 15 8 – 8 + m > 15 – 8 m > 7 Original inequality Subtract 8 from each side. Simplify. c. 8 + m > 15

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GUIDED PRACTICE for Examples 1 and 2 Graph and write a verbal phrase for the inequality. 1. z ≥ –1 SOLUTION InequalityGraphVerbal Phrase z ≥ –1 All numbers greater than or equal to –1 –3 –2 –1 0 1

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GUIDED PRACTICE for Examples 1 and 2 2. 4 > p SOLUTION InequalityGraphVerbal Phrase 4 > p All numbers less than 4. 2 3 4 5 6

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GUIDED PRACTICE for Examples 1 and 2 3. k –3.5 SOLUTION InequalityGraphVerbal Phrase k –3.5 All numbers less than or equal to –3.5. –5 –4 –3 –2 –1

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GUIDED PRACTICE for Examples 1 and 2 4. m > 1 2 SOLUTION InequalityGraphVerbal Phrase 1 2 m > All numbers greater than. 1 2 –2 –1 0 1 2

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GUIDED PRACTICE for Examples 1 and 2 5. x – 3 > –2 SOLUTION Original inequality Add 3 to each side. Simplify. x – 3 > – 2 x – 3 + 3> – 2+ 3 x > 1 Graph

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GUIDED PRACTICE for Examples 1 and 2 6. 6 > t – 1 SOLUTION Original inequality Add 1 to each side. Simplify. 6 > t – 1 6 + 1 > t – 1 + 1 7 >t Graph

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GUIDED PRACTICE for Examples 1 and 2 7. 12 ≥ p + 14 SOLUTION Original inequality Subtract 14 from each side. Simplify. 12 ≥ p + 14 – 14 ≥ p + 1412– 14 ≥ p –2 Graph

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GUIDED PRACTICE for Examples 1 and 2 8. x + 5 < 10 SOLUTION Original inequality Subtract 5 from each side. Simplify. x + 5 < 10 x + 5 < 10 – 5 x < 5 Graph x < 5 3 4 5 6 7

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GUIDED PRACTICE for Examples 1 and 2 9. t + 9 6 SOLUTION Original inequality Subtract 9 from each side. Simplify. t + 9 6 t + 9– 9 6 – 9 –3 t Graph

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GUIDED PRACTICE for Examples 1 and 2 10. –4 < k –3 SOLUTION Original inequality Add 3 to each side. Simplify. –4 < k – 3 < k – 3+ 3 –4 + 3< k –1 Graph

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Inequalities Objective: To solve and graph all types of inequalities.

Inequalities Objective: To solve and graph all types of inequalities.

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