Question 1

Which of the following best describes the solution set to the compound inequality $$-6x \leq -18 or$$ $$6x - 24 \geq 18$$?

Accepted Answer

The union of the solution sets of both inequalities.

Question 2

Solve the inequality $$-6x \leq -18. $$What is the solution set?

Accepted Answer

$$[3, \infty)$$

Question 3

Solve the inequality $$6x - 24 \geq 18. $$What is the solution set?

Accepted Answer

$$[7, \infty)$$

Question 4

What is the interval notation for the union of the solution sets $$[3, \infty)$$ and $$[7, \infty)$$?

Accepted Answer

$$[3, \infty)$$

Question 5

If a compound inequality uses the word 'or', which values are included in the solution set?

Accepted Answer

Values that satisfy either inequality or both.

Question 6

Which step is necessary when solving $$-6x \leq -18 to $$isolate $$x$$?

Accepted Answer

Multiply both sides by $$-1/6$$ and reverse the inequality.

Question 7

After solving $$6x - 24 \geq 18$$, what is the next step to isolate $$x$$?

Accepted Answer

Multiply both sides by $$1/6.$$

Question 8

Which of the following represents the graph of the solution set for $$-6x \leq -18$$?

Accepted Answer

A ray starting at 3 and extending to the right.

Question 9

If $$x = 5$$, which inequalities from the compound statement $$-6x \leq -18 or$$ $$6x - 24 \geq 18$$ does $$x$$ satisfy?

Accepted Answer

Only $$-6x \leq -18.$$

Question 10

If $$x = 8$$, which inequalities from the compound statement $$-6x \leq -18 or$$ $$6x - 24 \geq 18$$ does $$x$$ satisfy?

Accepted Answer

Both inequalities.

Question 11

Which real-world scenario best illustrates the use of a compound inequality with 'or'?

Accepted Answer

A driver can legally drive if they are at least 18 years old or have a special permit.

Question 12

Which of the following is NOT a correct method for finding the union of two solution sets?

Accepted Answer

Find the intersection of the solution sets.

Question 13

What is the correct interval notation for the solution set of $$x \geq 3 or$$ $$x \geq 7$$?

Accepted Answer

$$[3, \infty)$$

Question 14

If a compound inequality is written as $$A or$$ $$B$$, which symbol is used to denote the union of their solution sets?

Accepted Answer

$$\cup$$

Question 15

Which step is required when multiplying both sides of an inequality by a negative number?

Accepted Answer

Reverse the direction of the inequality.

Question 16

A compound inequality is solved and the solution sets are $$[3, \infty)$$ and $$[7, \infty). $$What is the union of these sets?

Accepted Answer

$$[3, \infty)$$

Question 17

Which of the following is a common mistake when solving $$-6x \leq -18$$?

Accepted Answer

Multiplying both sides by $$-1/6$$ without reversing the inequality.

Question 18

If a student solves $$6x - 24 \geq 18$$ and gets $$x \geq 3$$, what error did they likely make?

Accepted Answer

They incorrectly solved for $$x$$ after simplifying.

Question 19

Which of the following best describes the solution set for the compound inequality $$x \geq 3 or$$ $$x \geq 7$$?

Accepted Answer

All real numbers greater than or equal to 3.

Solving Compound Inequalities with 'Or' (Union)

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