Question 1

Which of the following best describes the intersection of two sets $$A$$ and $$B$$?

Accepted Answer

The set of all elements that are in both $$A$$ and $$B.$$

Question 2

Solve the compound inequality $$2x - 5 \u003e 1$$ and $$x + 3 \u003c 7. $$What is the solution set?

Accepted Answer

$$3 \u003c x \u003c 4$$

Question 3

If $$A = \{2, 4, 6, 8\}$$ and $$B = \{4, 6, 10\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{4, 6\}$$

Question 4

Solve and graph the solution for $$x + 2 \u003e 0$$ and $$2x \u003c 10.$$

Accepted Answer

$$x \u003e -2$$ and $$x \u003c 5$$

Question 5

Which of the following statements about the union of two sets $$A$$ and $$B is $$correct?

Accepted Answer

It contains all elements that are in $$A or$$ $$B or $$both.

Question 6

Solve the compound inequality $$3x - 4 \leq 5 or$$ $$x + 2 \geq 7.$$

Accepted Answer

$$x \leq 3 or$$ $$x \geq 5$$

Question 7

A chemical process is safe if the temperature $$T$$ satisfies $$20 \leq T \leq 80. $$Which of the following describes the solution set?

Accepted Answer

$$20 \leq T \leq 80$$

Question 8

Solve the compound inequality $$-2x + 6 \u003e 0$$ and $$x - 1 \u003c 4.$$

Accepted Answer

$$x  -3$$

Question 9

If $$A = \{1, 2, 3\}$$ and $$B = \{3, 4, 5\}$$, what is $$A \cup B$$?

Accepted Answer

$$\{1, 2, 3, 4, 5\}$$

Question 10

A patient’s blood pressure $$P$$ must be either below 90 or above 140 to require medication. Which compound inequality represents this scenario?

Accepted Answer

$$P  140$$

Question 11

Solve the compound inequality $$5 - 2x \leq 1$$ and $$x + 4 \u003e 0.$$

Accepted Answer

$$x \geq 2$$ and $$x \u003e -4$$

Question 12

Which of the following is true about the solution set of $$x  5$$?

Accepted Answer

It is the union of $$x  5.$$

Question 13

A factory must keep the humidity $$h$$ between 30% and 60% inclusive. Which compound inequality represents this requirement?

Accepted Answer

$$30 \leq h \leq 60$$

Question 14

Solve the compound inequality $$-3x \u003e 6 or$$ $$x + 2 \u003c 1.$$

Accepted Answer

$$x \u003c -2 or$$ $$x \u003c -1$$

Question 15

If $$A = \{2, 4, 6\}$$ and $$B = \{1, 2, 3, 4\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{2, 4\}$$

Question 16

A student must score at least 70 but less than 90 to pass a course with a 'B'. Which compound inequality represents this?

Accepted Answer

$$70 \leq x \u003c 90$$

Compound Inequalities: Intersection and Union of Sets

Study Guide - Practice Questions