1. Do Now: Solve and Graph

3. Solving & Graphing
Compound
Inequalities

4. 2 types of compound inequalities
“OR” Statements
Are only written separately using the word “OR”
Graphs can go in opposite directions, they do not have to cross.
Shading can continue past the circles.
“AND” Statements
Can be written separately using the word “AND”
Can be written together without using the word “AND”
Graphs must cross to show what each answer shares.
Shading stops at the circles

5. 1. Graph the solution set of X > -5 and x < 1.
FIRST, write a
Compound
Inequality !!
What kind of
Circle?
What kind of
Circle?
Now shade
Between the
circles !!
<---|---|---|---|---|---|---|---|---|---> -6 -5 -4 -3 -2 -1 1 2
When graphing COMPOUND INEQUALITIES ( the AND statements ), shading stops at the endpoints.

6. 2. Graph the solution set of m > -2 and m < 3.
FIRST, write a
Compound
Inequality !!
What kind of
Circle?
What kind of
Circle?
Now shade
Between the
circles !!
<---|---|---|---|---|---|---|---|---|---> -3 -2 -1 1 2 3 4 5
When graphing COMPOUND INEQUALITIES ( the AND statements ), shading stops at the endpoints.

7. 3. Solve and graph: x – 2 > - 4 and x + 2 < 5
FIRST, Solve each for x.
NEXT, Write a Compound Inequality.
NOW, graph it!!
<---|---|---|---|---|---|---|---|---|---> 5 -3 -2 -1 1 2 3 4

8. 4. Solve and graph x + 1 < 2 and -5x < 15
FIRST, Solve each for x.
NEXT, Write a Compound Inequality.
Start with the SMALLER number
NOW, graph it!!
<---|---|---|---|---|---|---|---|---|---> -3 -2 -1 1 2 3 4 5

9. 5. Solve and graph: <---|---|---|---|---|---|---|---|---|---> -5
FIRST, Solve for x.
Divide each term by 2.
NOW, graph it!!
<---|---|---|---|---|---|---|---|---|---> -5 -4 -3 -2 -1 1 2 3

10. 6. Solve and graph: <---|---|---|---|---|---|---|---|---|---> 8
Start in the middle and solve for x.
Now divide each term by 3.
<---|---|---|---|---|---|---|---|---|---> 1 2 3 4 5 6 7 8

11. Now, let’s look at “OR” statements
7. Graph x < -2 OR x > 5
<---|---|---|---|---|---|---|---|---|---> -3 -2 -1 1 2 3 4 5
And that’s it!! The graph shows that the answers are true for one statement OR the other.
The arrows show that the shading does not stop, and that the answers continue on in that direction.

12. 8. Graph: OR <---|---|---|---|---|---|---|---|---|--->-3 -2 -1 1 2 3 4 5
Since these “or” solutions happen to cross, you can simplify the graph to look like this.
<---|---|---|---|---|---|---|---|---|---> -3 -2 -1 1 2 3 4 5
…because x < 3 crosses over or “covers up” x < 1

13. 9. Solve and graph:
First, Solve for m. OR OR
<---|---|---|---|---|---|---|---|---|---> -3 -2 -1 1 2 3 4 5

14. 10. Solve and graph
First, Solve for x. OR
Turn your answer around OR
<---|---|---|---|---|---|---|---|---|---> -3 -2 -1 1 2 3 4 5