1. Compound Inequalities
What you’ll learn
To solve and graph inequalities containing the word
and. To solve inequalities containing the word or
Vocabulary
Compound inequality: A compound inequalities consists of two distinct inequalities joined by the word and or the word or.
Interval notation: includes the use
of the three special symbols.

2. Writing a compound inequality
Example 1:What compound inequality represents
the phrase? Graph the solutions.
All real numbers that are greater than -2 and
less than 6
n›-2 and n‹6
-2‹n and n‹6
-2‹n‹6
B. All real numbers that are less than 0 or greater
than or equal to 5
t‹0 or t≥5

3. Your turn
What compound inequality represents the phrase? Graph the solutions.
All real numbers that are greater than or equal
to -4 and less than 6
n≥-4 and n<6
-4≤n<6
B. All real numbers that are less than or equal to
or greater than 6
=2.5
n≤2.5 or n>6

4. Solving a compound inequality involving andor
Note: a solution of a compound inequality involving
and is any number that makes both inequalities true.
You can solve this inequality both ways.

5. Solving a compound inequality involving or
Note: A solution of a compound inequality involving or
is an number that makes either inequality true.
You must solve them separately.

6. Your turn
What are the solutions of? Graph the inequalities
A. -5 < 3y-4 < 14
Answers:
B.-2y+7 < 1 or 4y+3 ≤ -5
Answers: y>3 or y≤2

7. the compound inequality
Writing and Solving a Compound Inequality
To earn a B in your algebra course, you must achieve
an unrounded test average between 84 and 86,
inclusive. You scored 86,85, and 80 on the first three
test of the grading period. What possible scores can
you earn on the fourth and final test a B in the course
Need
Possible scores you
can earn
on the last test to
get a B in the course
Plan
Write an expression
for you test average.
Then write and solve
the compound inequality
Know
Test average must
be between 84 and 86,
inclusive.
The first 3 test scores
Your score on the fourth test must be between
85 and 93, inclusive

8. Your turn
To win the recycling contest, you must collect between 83 and 87 pop tabs each week, inclusive. Suppose you collected 82, 86,and 84 pop tabs during the first three weeks of the competition. What are the possible numbers of pop tabs you can collect during the fourth and final week in order to win the recycling contest?
Answer: between 80 and 96 pop tabs inclusive

9. Using Interval Notation
1.What is the graph [-4,6)? How do you write [-4,6)
as an inequality?
The parenthesis indicates that 6 is not included. So use an open circle at 6.
The bracket indicates
that -4 is included.
So use a closed
circle at -4.
-4 ≤ x < 6
2.What is the graph of x ≤ -1 or x>2? How do you
write x≤-1 or x>2 in interval notation.
The interval or

10. Classwork odd Homework even
Pgs exercises 9-41