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

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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

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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 DIDNT HAVE IT, SORRY! DID SHE KEEP HER PROMISE?

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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 DIDNT HAVE IT, SORRY! DID SHE KEEP HER PROMISE?

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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

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Writing Compound Inequalities (AND) Lets Break it Down

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Writing Compound Inequalities (OR)

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

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

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

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Lets Try (AND Ex. 1) -2 < x < 5 Break it up: x > -2 AND x < 5

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Lets Try (AND Ex. 2) -9 x < -1

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Lets Try (AND Ex. 3) -5 x 4

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Lets Try (OR Ex. 1) x 4 Break it up: x < -6 OR x > 4

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Lets Try (OR Ex. 2) x -1 or x > 3

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Lets Try (OR Ex. 3) x < -8 or x 8

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Questions?! HOMEWORK: Graphing Compound Inequalities Worksheet

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Compound Inequalities (cont.) SOLVING

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Solving a Compound Inequality with OR Solve both inequalities separately.

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Solving a Compound Inequality with OR 3x + 1 7

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

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

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

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

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

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

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Example 1 -2 < -3x 2 < 1

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Example 2 -8 < -6x 2 < 16

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