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.

Graph an Intersection

Answer:

A.

B.

C.

D.

Graph the solution set of t > 5 and t 8.≤

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

Answer:

A.

B.

C.

D.

Graph the solution set of a < 4 or a 7.≥

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 a Union

Answer:

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.

A.

B.

C.

D.

Graph the solution set of y < –24 or y ≥ 24 on a number line.

A.

B.

C.

D.

Graph the solution set of g ≤ 4 and g > 0 on a number line.

A.

B.

C.

D.

Graph the solution set of z < 25 or z ≤ 10 on a number line.

A.

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.

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