Lesson 6 Menu : Lesson 6 Menu Five-Minute Check (over Lesson 6-5)
Main Ideas
California Standards
Example 1: Solve an Absolute Value Inequality (<)
Example 2: Solve an Absolute Value Inequality (>)
Concept Summary: Absolute Value Equations and Inequalities
Example 3: Real-World Example
Lesson 6 MI/Vocab : Lesson 6 MI/Vocab Solve absolute value inequalities. Apply absolute value inequalities in real-world problems.
Lesson 6 CA : Lesson 6 CA Standard 3.0 Students solve equations and inequalities involving absolute values. (CAHSEE)
Lesson 6 Ex1 : Lesson 6 Ex1 Solve an Absolute Value Inequality (<) A. Solve |s – 3| ≤ 12. Then graph the solution set. Write |s – 3| ≤ 12 as s – 3 ≤ 12 and s – 3 ≥ –12. Answer: The solution set is {s | –9 ≤ s ≤ 15}. Case 1 Case 2 s – 3 ≤ 12 Original inequality s –3 ≥ –12 s – 3 + 3 ≤ 12 + 3 Add 3 to each side. s – 3 + 3 ≥ –12 + 3 s ≤ 15 Simplify. s ≥ –9
Lesson 6 Ex1 : Lesson 6 Ex1 Solve an Absolute Value Inequality (<) B. Solve |x + 6| < –8. Since |x + 6| cannot be negative, |x + 6| cannot be less than –8. So, the solution is the empty set Ø. Answer: Ø
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D A. Solve |p + 4| < 6. Then graph the solution set.
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D B. Solve |p – 5| < –2.
Lesson 6 Ex2 : Lesson 6 Ex2 Solve an Absolute Value Inequality (>) A. Solve |3y – 3| > 9. Then graph the solution set. Original inequality Add 3 to each side. Simplify. Divide each side by 3. Simplify. Case 1 3y – 3 is positive. Case 2 3y – 3 is negative.
Lesson 6 Ex2 : Lesson 6 Ex2 Solve an Absolute Value Inequality (>) Answer: The solution set is {y | y < –2 or y > 4}.
Lesson 6 Ex2 : Lesson 6 Ex2 Solve an Absolute Value Inequality (>) B. Solve |2x + 7| ≥ –11. Answer: Since |2x + 7| is always greater than or equal to 0, the solution set is {x | x is a real number}.
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D A. Solve |2m – 2| > 6. Then graph the solution set.
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D B. Solve |5x – 1| ≥ –2.
Lesson 6 CS1 : Lesson 6 CS1
Lesson 6 Ex3 : Lesson 6 Ex3 The average annual rainfall in California for the last 100 years is 23 inches. However, the annual rainfall can differ by 10 inches from the 100 year average. What is the range of annual rainfall for California? The difference between the actual rainfall and the average is less than or equal to 10. Let x be the actual rainfall in California. Then |x – 23| ≤ 10. Case 1
x – 23 ≤ 10
x – 23 + 23 ≤ 10 + 23
x ≤ 33 Case 2
–(x – 23) ≤ 10
x – 23 ≥ –10
x – 23 + 23 ≥ –10 + 23
x ≥ 13
Lesson 6 Ex3 : Lesson 6 Ex3 Answer: The range of rainfall in California is {x |13 x 33}.
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D A. {x | 70 ≤ x ≤ 74}
B. {x | 68 ≤ x ≤ 72}
C. {x | 68 ≤ x ≤ 74}
D. {x | 69 ≤ x ≤ 75} A thermostat inside Macy’s house keeps the temperature within 3 degrees of the set temperature point. If the thermostat is set at 72 degrees Fahrenheit, what is the range of temperatures in the house?
End of Lesson 6 : End of Lesson 6