Download - Compound Inequalities
Compound InequalitiesGoal: Write, solve and graph
compound inequalities.
Prepare to have your mind blown!!
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
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?
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?
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
Writing Compound Inequalities (AND)
• Let’s Break it Down
Real Life Compound Inequalities
Write and inequality to describe the Alpine meadow region. (use y is represent region)
Real Life Compound Inequalities
Write and inequality to describe the Timber Region. (use y is represent region)
Graphing Compound Inequalities
• AND connect together (one line segment)• OR two separate lines
Let’s Try (AND Ex. 1) -2 < x < 5
Break it up: x > -2 AND x < 5
Let’s Try (AND Ex. 2) -9 ≤ x < -1
Let’s Try (AND Ex. 3) -5 ≤ x ≤ 4
Let’s Try (OR Ex. 1) x < -6 or x > 4
Break it up:x < -6ORx > 4
Let’s Try (OR Ex. 2) x ≤ -1 or x > 3
Let’s Try (OR Ex. 3) x < -8 or x ≥ 8
Questions?!HOMEWORK:Graphing Compound Inequalities Worksheet
Compound Inequalities (cont.)
SOLVING
Solving a Compound Inequality with OR
• Solve both inequalities separately.
Solving a Compound Inequality with OR
3x + 1 < 4 or 2x – 5 > 7
Solving a Compound Inequality with OR – Ex. 2
• Solve both inequalities separately.
2x + 3 < -1 or 3x – 5 > -2
Solving a Compound Inequality with OR – Ex. 3
2x - 1 < -7 or 7x – 7 > 7
Solving Compound Inequalities with AND
• Do all steps to all parts of inequality.
-2 ≤ 3x – 8 ≤ 10
Solving Compound Inequalities with AND – Ex. 2
7 < x + 4 < 8
Solving Compound Inequalities with AND – Ex. 3
-15 < 2x - 5 < 9
Multiplying or Dividing by a Negative
•When multiplying or dividing a compound inequality by a negative you MUST SWITCH BOTH SIGNS!!!!
Example 1
-2 < -3x – 2 < 1
Example 2
-8 < -6x – 2 < 16
Homework •Pg. 349 Numbers 12 – 24
evens–SHOW WORK!!