1. 4.1.2 – Compound Inequalities

2. Recall from yesterday, to solve a linear- inequality, we solve much like we solve an equation – Isolate the variable – Inverse operations – Flip sign when multiply/divide by a negative number – Open vs. Closed dots

3. Compound Inequalities We can combine different inequalities to form compound inequalities Two cases to consider 1) AND 2) OR

4. AND An “AND” inequality will be one of the form a < x < b OR a ≤ x ≤ b On the number line:

5. To solve an AND problem, we usually keep it as one inequality Basically like operating with two equal signs What we do to the middle, we must do to BOTH sides If you divide or multiply by a negative number, BOTH signs will flip

6. Example. Solve the inequality 4 < x + 5 < 7. Graph your solutions on a number line.

7. Example. Solve the inequality -8 ≤ x – 10 ≤ -2. Graph your solutions on a number line.

8. Example. Solve the inequality -1 ≤ -m + 2 ≤ -3. Graph your solutions on a number line.

9. OR With an OR problem, we will essentially have two separate inequalities x b Graph of solutions:

10. Example. Solve the inequality 3x + 2 3. Graph your solutions on the number line.

11. Example. Solve the inequality -x > 4 OR -2x – 6 < 0. Graph your solutions on the number line.

12. Assignment Pg. 176 34-37, 40-42, 49-56, 61