1. Algebra 1
Section 4.4

2. Compound Sentences
In mathematics, a compound sentence is made by connecting two statements using the word and or the word or.

3. Definition
A conjunction is a compound sentence consisting of mathematical statements connected by the word and.

4. Conjunctions
In order for a conjunction to be true, both parts must be true.
The intersection—the values that are in both solutions— forms the solution to the conjunction.

5. Graph the solution set of
Example 1
Graph the solution set of
x > -1 and x ≤ 4.

6. Example 1
-1 < x ≤ 4
-1 is less than x, which is less than or equal to 4
The symbol  is often used for the word and.

7. Example 2 Graph and state the solution to x ≥ 5  x < 0.
Ø: No points in the solution set

8. Solve and graph the solution set of
Example 3
Solve and graph the solution set of
2x + 5 ≤ 11 and -3x > 18.
2x ≤ 6
x ≤ 3
x < -6
x ≤ 3  x < -6

9. Example 3
x ≤ 3  x < -6

10. Example 4 The combined conjunction -1 < 3x + 5 < 8
can be separated into two inequalities separated by the word and:
-1 < 3x + 5 and 3x + 5 < 8

11. Example 4
The steps to solve this conjunction can be applied to the combined conjunction, or to the separate inequalities.
-1 < 3x + 5 < 8
-1 < 3x + 5 and 3x + 5 < 8

12. In Example 4, both inequalities required the same steps to solve.
In Example 5, different steps are required; therefore, the inequalities must be written separately.

13. Example 5 x – 3 ≤ 2x – 9 < 15 x – 3 ≤ 2x – 9 and 2x – 9 < 15

14. Example 5
x ≥ 6 and x < 12
x ≥ 6  x < 12
6 ≤ x < 12

15. This problem involves a range of values.
Example 6
This problem involves a range of values.
Brittany’s grade must be at least 80, but less than 90, to get a B in the class.
80 ≤ grade < 90

16. Let t = the score on the 3rd test
Example 6
Let t = the score on the 3rd test
80 ≤ < 90 t 3
240 ≤ t < 270
82 ≤ t < 112

17. Example 6 82 ≤ t < 112 She must get at least an 82.
An 82 would get her an average of exactly 80.
A grade of 112 is needed for an A; this is not possible.

18. Homework: pp