Compound Inequalities Goal: 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

Writing Compound Inequalities (OR)

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 4  Break it up: x < -6 OR x > 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 7

Solving a Compound Inequality with OR – Ex. 2 Solve both inequalities separately. 2x

Solving a Compound Inequality with OR – Ex. 3 2x - 1 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 < 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!!