Question 1

Which of the following best describes a compound inequality?

Accepted Answer

Two inequalities joined by the words 'and' or 'or'.

Question 2

Given $$A = \{2, 4, 6, 8\}$$ and $$B = \{4, 5, 6, 7\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{4, 6\}$$

Question 3

Solve the compound inequality: $$1 \leq x + 7 \leq 10. $$What is the solution set in interval notation?

Accepted Answer

$$[-6, 3]$$

Question 4

Which of the following statements about the intersection of two sets is correct?

Accepted Answer

It includes only the elements that are in both sets.

Question 5

Solve the compound inequality: $$2x - 3 \geq 1$$ and $$x + 4 \u003c 10. $$What is the solution set in interval notation?

Accepted Answer

$$[2, 6)$$

Question 6

Given $$C = \{2, 3, 4, 5\}$$ and $$D = \{4, 5, 6, 7\}$$, what is $$C \cup D$$?

Accepted Answer

$$\{2, 3, 4, 5, 6, 7\}$$

Question 7

Which of the following best describes the union of two sets?

Accepted Answer

The set of elements that belong to either or both sets.

Question 8

Solve the compound inequality: $$3x + 2 \leq 5 or$$ $$7x - 2 \u003e 9. $$Express the solution in interval notation.

Accepted Answer

$$(-\infty, 1] \cup (\frac{11}{7}, \infty)$$

Question 9

A medical researcher is analyzing patient ages. Let $$A be $$the set of patients aged 20 to 40, and $$B be $$the set of patients aged 35 to 60. What is $$A \cap B$$?

Accepted Answer

$$[35, 40]$$

Question 10

Solve the compound inequality: $$-2 \u003c 3x + 1 \leq 7. $$Express the solution in interval notation.

Accepted Answer

$$(-1, 2]$$

Question 11

A chemical process is safe if the temperature $$T$$ satisfies $$T  100. $$Which interval notation represents all safe temperatures?

Accepted Answer

$$(-\infty, 50) \cup (100, \infty)$$

Question 12

Solve the compound inequality: $$2 \leq 4x + 6 \u003c 18. $$Express the solution in interval notation.

Accepted Answer

$$[-1, 3)$$

Question 13

Which of the following is the correct solution to the compound inequality $$x - 2 \u003e 3 or$$ $$2x + 1 \u003c 5$$?

Accepted Answer

$$(-\infty, 2) \cup (5, \infty)$$

Question 14

A city enforces a noise ordinance where noise levels must be below 60 dB or above 120 dB to avoid fines. Which set represents the safe noise levels?

Accepted Answer

$$(-\infty, 60) \cup (120, \infty)$$

Question 15

Solve the compound inequality: $$5 \u003c 2x + 1 \leq 13. $$Express the solution in interval notation.

Accepted Answer

$$(2, 6]$$

Question 16

If $$A = \{x | x 	ext{ is an even integer}\}$$ and $$D = \{4, 5, 6, 7\}$$, what is $$A \cap D$$?

Accepted Answer

$$\{4, 6\}$$

Question 17

Which of the following is the correct interval notation for the solution to $$-3 \leq 2x - 1 \u003c 7$$?

Accepted Answer

$$[-1, 4)$$

Question 18

A student must score at least 70 but less than 90 on an exam to pass with distinction. Let $$x be $$the score. Which compound inequality represents this requirement?

Accepted Answer

$$70 \leq x \u003c 90$$

Question 19

Solve the compound inequality: $$x + 2 \u003e 5 or$$ $$2x - 1 \u003c 3. $$Express the solution in interval notation.

Accepted Answer

$$(-\infty, 2) \cup (3, \infty)$$

Compound Inequalities: Intersection and Union of Sets

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