Lesson Menu Main Idea and New Vocabulary NGSSS Example 1:Write Compound Inequalities Example 2:Graph an Intersection Example 3:Write Compound Inequalities Example 4:Graph a Union Example 5:Graph a Union Five-Minute Check

Main Idea/Vocabulary Write and graph compound inequalities in one variable. compound inequality intersection union

NGSSS MA.8.A.4.2 Solve and graph one- and two- step inequalities in one variable.

Example 1 Write Compound Inequalities PASTA Angela is cooking pasta. The cooking directions state the pasta should be cooked in boiling water for at least 7 minutes and no more than 10 minutes. Write a compound inequality to represent this situation. Answer:Since m ≥ 7 and m ≤ 10, the compound inequality is 7 ≤ m ≤ 10.

Example 1 CYP A.9 ≤ h ≤ 157 B.9 < h < 157 C.h ≥ 157 or h ≤ 9 D.h ≥ 9 and h ≥ 157 ROLLER COASTER The height of a roller coaster is at least 9 feet and goes up to 157 feet. Write a compound inequality to represent this situation.

Example 2 Graph the solution set of x < 4 and x ≥ 2. Graph an Intersection Graph x < 4. Graph x ≥ 2. Find the intersection. The intersection is all real numbers greater than or equal to 2 but less than 4.

Example 2 Graph an Intersection Answer:

Example 2 CYP A. B. C. D. Graph the solution set of t > 5 and t 8. ≤

Example 3 Write Compound Inequalities SALES A store’s computer prints a special report if the number of sales are less than 5 or greater than 20. Write a compound inequality to represent this situation. Let s represent the number of sales. Answer: The compound inequality is s 20.

Example 3 CYP A.40 ≤ t < 85 B.40 ≥ t > 85 C.t > 85 or t ≤ 40 D.t ≥ 85 or t < 40 PAINT Outdoor painting should not be done if the temperature is above 85  F or 40  F or less. Write a compound inequality to represent this situation.

Example 4 Graph the solution set of n ≥ 2 or n ≤ –3. Graph a Union Graph both inequalities to find the union. Graph n ≥ 2. Graph n ≤ –3. Find the union. The union is all real numbers less than or equal to –3 or greater than or equal to 2.

Example 4 Graph a Union Answer:

Example 4 CYP A. B. C. D. Graph the solution set of a < 4 or a 7. ≥

Example 5 Graph a Union Graph the solution set of c > –2 or c ≥ 1. Graph both simple inequalities to find the union. Graph c > –2. Graph c ≥ 1. Find the union. The union is all real numbers greater than –2.

Example 5 Graph a Union Answer:

Example 5 CYP A. B. C. D. Graph the solution set of t < –10 or t –8. ≤

Graph the solution set of f > –5 and f < 10 on a number line. Five Minute Check 1 A. B. C. D.

Graph the solution set of y < –24 or y ≥ 24 on a number line. Five Minute Check 2 A. B. C. D.

Graph the solution set of g ≤ 4 and g > 0 on a number line. Five Minute Check 3 A. B. C. D.

Graph the solution set of z < 25 or z ≤ 10 on a number line. Five Minute Check 4 A. B. C. D.

A.a > 3 and a < 12 B.a ≥ 3 and a < 12 C.a 12 D.a ≤ 3 and a ≥ 12 To order from the children’s menu at a local restaurant, a child must be at least three years old, and be less than twelve years old. Write a compound inequality to represent this situation. Five Minute Check 5