1. Chapter 3: Solving Inequalities
Section 3.6: Compound Inequalities

2. Day 1

3. Compound Inequalities
A Compound Inequality consists of two distinct inequalities joined by the word and or the word or. You find the solutions of a compound inequality either by identifying where the solution sets of the distinct inequalities overlap(and) or by combining the solution sets to form a larger solution set(or). and – Where the graphs Overlap or Combine the graphs

4. Writing Compound Inequalities
What compound inequality represents the phrase and graph the solutions. All real numbers that are greater than -2 AND less than 6. n > -2 n < 6 -2 < n < 6

5. Writing Compound Inequalities
What compound inequality represents the phrase and graph the solutions. All real numbers that are less than 0 OR greater than or equal to 5. n < 0 n ≥ 5 n < 0 or n ≥𝟓

6. Solving Compound Inequalities (AND)
What are the solutions of −3 ≤𝑚 −4 <−1? Graph the solutions! Break it up into two inequalities!! -3 ≤ m – 4 and m – 4 < ≤ m m < 3 1 ≤ m < 3

7. Solving Compound Inequalities (AND) – You Try!!!
What are the solutions of −2<3𝑦 −4 <14? Graph the solutions! Break it up into two inequalities!! -2 < 3y – 4 and 3y – 4 < < 3y 3y < < y y < < y < 6

8. Solving Compound Inequalities (OR)
What are the solutions of 3𝑡+2 <−7 𝑜𝑟 −4𝑡+5 <1? Graph the solutions.
3𝑡+2 <−7 or −4𝑡+5 <1
3𝑡 <− −4𝑡 <−4
t < t > 1
𝑡<−3 𝑜𝑟 𝑡 >1

9. Solving Compound Inequalities (OR) – You Try!!!
What are the solutions of −2𝑦+7 <1 𝑜𝑟 4𝑦+3 ≤−5 ? Graph the solutions.
−2𝑦+7 <1 or 4𝑦+3 ≤−5
−2𝑦<− 𝑦≤−8
y > y ≤ -2
𝑦≤−2 𝑜𝑟 𝑦 >3

10. Day 1 Homework!!!
Page 204: 1, 2, 9, 11-14, 17-19

11. To Start: 10 Points
Solve and Graph:
5𝑦+7 ≤−3 𝑜𝑟 3𝑦 −2 ≥13

12. Day 2

13. Interval Notation
You can use an inequality such as x < -3 to describe a portion of the number line called an interval. You can also use Interval Notation to describe an interval on the number line using three special symbols.

14. Interval Notation
Write [-4,6) as an inequality and graph the solution. [ = ≤𝑜𝑟 ≥ Since it starts the inequality, the first part is −4 ≤ x The ending is 6) therefore the second part is x < 6. −4 ≤𝑥<6

15. Interval Notation (-∞,-1] or (2,∞) Interval Notation:
What is the graph of x ≤ -1 or x > 2? Also write it in Interval Notation.
Interval Notation:
(-∞,-1] or (2,∞)

16. Interval Notation – You Try!
What is the graph of (-2,7] and how do you write the inequality? x would be between -2 and 7 with the first inequality being < and the second being ≤ -2 < x ≤ 7

17. Homework!!!
Page 204: 5, 21-25, 27-29, 31, 32