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Compound Inequalities Goal: Write, solve and graph compound inequalities. Prepare to have your mind blown!!

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Presentation on theme: "Compound Inequalities Goal: Write, solve and graph compound inequalities. Prepare to have your mind blown!!"— Presentation transcript:

1 Compound Inequalities Goal: Write, solve and graph compound inequalities. Prepare to have your mind blown!!

2 What are Compound Inequalities? Compound Inequalities: two inequalities connected by and or or. Example: x is less than five and greater than -10 or -10 < x < 5

3 THE “OR” STORY LETS NOW SUPPOSE THAT YOU HAD EXHIBITED SUCH GOOD BEHAVIOR THAT YOUR MOM TOLD YOU THAT SHE WOULD GO TO WALMART OR K- MART TO TRY TO FIND YOU A NEW GAME THAT YOU HAVE BEEN WANTING FOR MONTHS. …SHE LATER TOLD YOU THAT SHE WENT TO K MART AND THEY DIDN’T HAVE IT, SORRY! DID SHE KEEP HER PROMISE?

4 THE “AND” STORY SUPPOSE THAT YOU HAD EXHIBITED SUCH GOOD BEHAVIOR THAT YOUR MOM TOLD YOU THAT SHE WOULD GO TO WALMART AND K-MART TO TRY TO FIND YOU A NEW GAME THAT YOU HAVE BEEN WANTING FOR MONTHS. …SHE LATER TOLD YOU THAT SHE WENT TO K MART AND THEY DIDN’T HAVE IT, SORRY! DID SHE KEEP HER PROMISE?

5 Writing Compound Inequalities From Words x is greater than 2 and less than or equal to 10 x is less than -7 or greater than 3

6 Writing Compound Inequalities (AND) Let’s Break it Down

7 Writing Compound Inequalities (OR)

8 Real Life Compound Inequalities Write and inequality to describe the Alpine meadow region. (use y is represent region)

9 Real Life Compound Inequalities Write and inequality to describe the Timber Region. (use y is represent region)

10 Graphing Compound Inequalities AND  connect together (one line segment) OR  two separate lines

11 Let’s Try (AND Ex. 1) -2 < x < 5  Break it up: x > -2 AND x < 5

12 Let’s Try (AND Ex. 2) -9 ≤ x < -1

13 Let’s Try (AND Ex. 3) -5 ≤ x ≤ 4

14 Let’s Try (OR Ex. 1) x 4  Break it up: x < -6 OR x > 4

15 Let’s Try (OR Ex. 2) x ≤ -1 or x > 3

16 Let’s Try (OR Ex. 3) x < -8 or x ≥ 8

17 Questions?! HOMEWORK: Graphing Compound Inequalities Worksheet

18 Compound Inequalities (cont.) SOLVING

19 Solving a Compound Inequality with OR Solve both inequalities separately.

20 Solving a Compound Inequality with OR 3x + 1 7

21 Solving a Compound Inequality with OR – Ex. 2 Solve both inequalities separately. 2x + 3 -2

22 Solving a Compound Inequality with OR – Ex. 3 2x - 1 7

23 Solving Compound Inequalities with AND Do all steps to all parts of inequality. -2 ≤ 3x – 8 ≤ 10

24 Solving Compound Inequalities with AND – Ex. 2 7 < x + 4 < 8

25 Solving Compound Inequalities with AND – Ex. 3 -15 < 2x - 5 < 9

26 Multiplying or Dividing by a Negative When multiplying or dividing a compound inequality by a negative you MUST SWITCH BOTH SIGNS!!!!

27 Example 1 -2 < -3x – 2 < 1

28 Example 2 -8 < -6x – 2 < 16

29 Homework Pg. 349 Numbers 12 – 24 evens – SHOW WORK!!


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