1. LESSON 3-6 COMPOUND INEQUALITIES
Objective: To solve and graph inequalities containing “and” or “or”.

2. Vocabulary
compound inequality – two inequalities joined by the word and or the word or
solution for and inequalities – (Intersection) any number that makes both inequalities true
solution for or inequalities – (Union) any number that makes either inequality true

3. STEPS for AND problems
Write the compound inequality as two inequalities joined by and.
Solve each inequality.
Simplify and write the solutions as one statement.
Graph the solution.

4. Translate the verbal phrase into an inequality
Translate the verbal phrase into an inequality. Then graph the inequality. a.
All real numbers that are greater than – 2
and less than 3.
Inequality:
– 2 < x < 3
Graph: b.
All real numbers that are less than 0 or greater than
or equal to 2.
x < 0 or x ≥ 2
Inequality:
Graph:

5. All real numbers that are less than –1 or greater than or equal to 4.c.
Inequality:
x < –1 or x ≥ 4 d.
All real numbers that are greater than or equal
To –3 and less than 5.
Inequality:
x ≥ –3 and x < 5
= –3 ≤ x < 5

6. Write and graph a real-world inequality:
CAMERA CARS
A crane sits on top of a camera car and faces toward the front. The crane’s maximum height and minimum height above the ground are shown. Write and graph a compound inequality that describes the possible heights of the crane.

7. Write and graph a real-world inequality:
SOLUTION
Let h represent the height (in feet) of the crane. All possible heights are greater than or equal to 4 feet and less than or equal to 18 feet. So, the inequality is 4 ≤ h ≤ 18.

8. You try… Solve each inequality and graph the solution.
1) -6 < 3x < 15 2) -3 < 2x-1 < 7

9. You try…
3) 7 < -3a + 1 < 13
Solution: -4 < n < -2

10. You try… 4) The books were priced between $3.50 and $6.00, inclusive.
Solution: < b < 6

11. To solve OR problems, solve each inequality separately.
5) Solve –2x + 7 > 3 or 3x – 4 > 5.

12. Which inequalities describe the following graph?-2 -1 -3 o
y > -3 or y < -1
y > -3 and y < -1
y ≤ -3 or y ≥ -1
y ≥ -3 and y ≤ -1
Answer Now

13. Which is equivalent to -3 < y < 5?
y > -3 or y < 5
y > -3 and y < 5
y < -3 or y > 5
y < -3 and y > 5
Answer Now

14. Which is equivalent to x > -5 and x ≤ 1?
Answer Now

15. Summary Re-write the compound inequality into two problems and solve.
For and problems, combine the solutions into one statement.
For or problems, solve each separately.
Graph.

16. Explain the difference between “and” vs. “or” compound inequalities.
Exit Ticket
Explain the difference between “and” vs. “or” compound inequalities.
How do you solve a compound inequality?

17. Homework:
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#’s odd