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12.5: Compound Inequalities

12.5: Compound Inequalities. Warmup. Identify the mistake in Alexis’ work below (circle the incorrect step and identify why it’s wrong): -(x-12)>12 Alex’s answer: -x+12 >12 -x>24 x<-24. Warmup. How could you represent the following statement using x and inequality symbols.

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12.5: Compound Inequalities

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  1. 12.5: Compound Inequalities

  2. Warmup Identify the mistake in Alexis’ work below (circle the incorrect step and identify why it’s wrong): -(x-12)>12 Alex’s answer: -x+12 >12 -x>24 x<-24

  3. Warmup How could you represent the following statement using x and inequality symbols. “To participate in the activity, you must be at least 13 years old and no more than 17 years old.”

  4. Application: John wants to give his dog vitamins. The daily dose is based on the dog’s weight. Use the information below to write an inequality for each weight category. Inequality Daily Dose Dog’s Weight ( pounds) _____________ 1 tablet 25 lbs or less _____________ 2 tablets greater than 25lbs and less than or equal to 50 lbs _____________ 3 tablets more than 50 lbs

  5. The inequality in the middle represents a compound inequality. Compound Inequalities: When 2 inequalities are combined with the words _”and”__ or _”or”__. A compound inequality with _and_ is true if and only if _both_ inequalities are true. The graph is the intersection of the 2 graphs.

  6. Examples of and vs or statements: Ex. 1: To pay adult price at the movies, you must be at least 20 and younger than 64 Ex. 2: To ride the kids swings at Hershey Park you must be at least a hershey kiss and no more than a hershey bar. Ex. 3: To pay cheaper ticket prices, you must be no less than 64 years old or no more than 5 years old Ex. 4: You are a minor until you are 18. Ex. 5: Laboratory alarms are set to go off if the temperature of chemicals exceed 72 degrees or drop below 60 degrees.

  7. Ex 1) Graph the compound inequality below. Rewrite the compound inequality without using the word “ and “. ___________________

  8. Ex 2)   ___________________

  9. Ex. 3

  10. Solve and graph the solution.

  11. Another type of compound inequality uses the word “ or “. This type of inequality is true if one or more of the inequalities is true. The graph is the union of the two graphs. Ex 5) Graph the solution of .

  12. Ex 6) Graph the solution of .

  13. Sometimes you must solve compound inequalities before graphing. • Ex 7) Solve or . Graph your solutions.

  14. Ex 8) Application: A pilot is flying at 30,000 feet and is told by the control tower that he should increase his altitude to at least 33,000 feet or decrease his altitude to no more than 26,000 feet to avoid some turbulence. Write and graph a compound inequality that describes this.

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