Section 3.6- Compound Inequalities
Essential Question: Why do inequalities have different kinds of solutions?
Do Now:
Key Concept: The Difference between ‘And’ and ‘Or’ in Inequalities
The graph of a compound inequality with
The graph of a compound inequality with
the word ____________ contains the
the word ____________ contains
___________________ of the graphs of the
________________ of the graphs of the two
two inequalities that form the compound
inequalities that form the compound
inequality.
inequality.
On number line, it looks like a _______
_____________.
On a number line, it looks like ______
_________.
Graph
Inequality
Graph
Inequality
NOTE: Inclusive means the solution ______________ the both endpoints in the
__________ case of compound inequalities
Example 1: Writing a Compound Inequality
What compound inequality represents the phrase? Graph the solutions.
a. all real numbers that are greater than -2 and less than 6.
b. all real numbers that are less than 0 or greater than or equal to 5.
c. all real numbers that are greater than or equal to -4 and less than 6.
1
d. all real numbers that are less than or equal to 2 2 or greater than 6
e. What is the difference between “x is between -5 and 7” and “x is between -5 and 7,
inclusive?”
Example 2: Solving a Compound Inequality Involving And
a. What are the solutions of −3 ≤ 𝑚 − 4 ≤ −1? Graph the solutions.
b. What are the solutions of −2 ≤ 3𝑦 − 4 < 14? Graph the solutions.
Example 3: Solving a Compound Inequality Involving Or
a. What are the solutions of 3𝑡 + 2 < −7 or −4𝑡 + 5 < 1? Graph the solutions.
b. What are the solutions of −2𝑦 + 7 < 1 or 4𝑦 + 3 ≤ −5? Graph the solutions.
Example 4: Writing and Solving a Compound Inequality
Suppose you scored 78, 78, and 79 on the first three tests. Is it possible for you to earn a
B in the course? Assume that 100 is the maximum grade you can earn in the course and
on the test. Explain.
NOTE: A ‘B’ in the course is between 84 and 86, inclusive.
Group Work:
Complete #1-3, 7 (ignore writing in interval notation).
HW: p. 204-205 #9, 10, 12-22 evens, 31-37, 42