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
• Write and graph compound inequalities in one variable.
• compound inequality
• intersection
• union
MA.8.A.4.2 Solve and graph one- and two-step inequalities in one variable.
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.
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.
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.
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 < 5 or s > 20.
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 85F or 40F or less. Write a compound inequality to represent this situation.
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.
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.
Graph the solution set of f > –5 and f < 10 on a number line.
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B.
C.
D.
Graph the solution set of y < –24 or y ≥ 24 on a number line.
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B.
C.
D.
Graph the solution set of g ≤ 4 and g > 0 on a number line.
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B.
C.
D.
Graph the solution set of z < 25 or z ≤ 10 on a number line.
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B.
C.
D.
A. a > 3 and a < 12
B. a ≥ 3 and a < 12
C. a < 3 and 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.