1. 4-5: Compound Inequalities
Essential Question: Explain the difference between compound inequalities with “and” and those with “or”.

2. 4-5: Compound Inequalities
Two inequalities that are joined by the word and or the word or form a compound inequality.
You can write the compound inequality x > -5 and x < 7 as -5 < x < 7
An “and” inequality has two “ends” when graphed

3. 4-5: Compound Inequalities
Example 1: Writing a Compound Inequality
All real numbers that are at least -2 and at most 4
n > -2 and n < 4
-2 < n < 4
Today’s high temperature will be above 32º F, but not as high as 40º F
32 < t < 40

4. 4-5: Compound Inequalities
Your Turn
Write a compound inequality that represents each situation. Then graph your solution.
All real numbers greater than -2 but less than 9
-2 < x < 9
The books were priced between $3.50 and $6.00, inclusive
3.50 < x < 6.00

5. 4-5: Compound Inequalities
A solution to an “and” inequality is any number that makes both inequalities true. One way you can solve a compound inequality is by writing two equations.
Example 2: Solving a Compound Inequality containing “And”
-4 < r – 5 < -1
-4 < r – And r – 5 < -1
1 < r r < 4
1 < r < 4

6. 4-5: Compound Inequalities
Your Turn
Solve each inequality. Graph your solution.
-6 < 3x < 15
-2 < x < 5
-3 < 2x – 1 < 7
-1 < x < 4

7. 4-5: Compound Inequalities
A solution of a compound inequality containing “or” is any number that makes either inequality true.
Example 4: Writing a Compound Inequality
All real numbers that are at most 3 or greater than 7
n < 3 or n > 7
An “or” inequality has two “oars” (like with a boat) when graphed

8. 4-5: Compound Inequalities
Your Turn
Write a compound inequality that represents each situation. Then graph your solution.
All real numbers that are at most -5 or at least 3
n < -5 or n > 3

9. 4-5: Compound Inequalities
To solve “or” inequalities, simply solve the two inequalities separately.
Example 5: Solving a Compound Inequality containing “Or”
4v + 3 < -5 Or -2v + 7 < 1
4v < v < -6
÷4 ÷4 ÷-2 ÷-2
v < -2 Or v > 3

10. 4-5: Compound Inequalities
Assignment
Worksheet 4-5
1 – 17 and 23 – 37
Odd Problems