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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 DIDN’T 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 DIDN’T 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) Let’s 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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Let’s Try (AND Ex. 1) -2 < x < 5 Break it up: x > -2 AND x < 5
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Let’s Try (AND Ex. 2) -9 ≤ x < -1
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Let’s Try (AND Ex. 3) -5 ≤ x ≤ 4
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Let’s Try (OR Ex. 1) x 4 Break it up: x < -6 OR x > 4
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Let’s Try (OR Ex. 2) x ≤ -1 or x > 3
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Let’s 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!!
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