Do Now: Solve and Graph.

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Presentation transcript:

Do Now: Solve and Graph

Solving & Graphing Compound Inequalities

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

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.

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.

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

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

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

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

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.

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

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

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