1. Compound Inequalities
CA 5.0

2. Objective - To solve compound inequalities involving “and”.

3. ABSOLUTE VALUE INEQUALITIES
 ALWAYS isolate the absolute value FIRST!
 NEVER distribute into absolute value!
 Absolute value equations usually have 2 answers!
│stuff│= pos solutions
│stuff│= solution
│stuff│= neg no solution
 FORM:
Variable / Symbol / Number
 When multiplying or dividing by a negative number you MUST flip the inequality symbol!
 Less th“and”
“and” where things overlap
 Great“or”
“or” everything together
symbol
>
< ≥ ≤
arrows
ABSOLUTE VALUE
INEQUALITIES

4. Curriculum Vocabulary
Compound Inequality:
An inequality the is formed by the union ∪ (“or”) or the intersection ∩ (“and”) of two simple inequalities.
Conjunction:
Disjunction:

5. N.B. The numbers MUST be written in order, as on a number line!
Write a compound inequality that describes all
the real numbers greater than -2 and less than 5.
and
“In-between
statement”
N.B. The numbers MUST be written in order, as on a number line!

6. Write the following compound inequalities as
“In Between” statements. 1) 2) 3)

7. Solve and graph the compound inequality.

8. Solve and graph.

9. Solve and graph.

10. A racquetball club charges a $20 membership
and $2 per hour. How many hours per month
can be played on a budget of $50 to $70?
Let x = # of hours
C = total cost
C = x
You can play from 15 to 25 hours per month