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

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 < -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!!