Graphing the compound inequality x ≤ 2 and x ≥ 5 yields which solution set?

Graphing the compound inequality x ≤ 2 and x ≥ 5 yields which solution set?

• A. Empty set
• B. {2}
• C. All real numbers
• D. Interval [2,5]

Answer: (A)

To solve a compound inequality, you look for numbers that satisfy both conditions at once—the intersection of the two sets. One condition says x is at most 2, and the other says x is at least 5. Numbers that are at most 2 lie to the left of or at 2 on the number line, while numbers that are at least 5 lie to the right of or at 5. There is no number that can be both at most 2 and at least 5 simultaneously, so the two regions do not overlap. On the number line, there’s a gap between 2 and 5 where neither condition holds. Therefore, no real number satisfies both requirements, and the solution set is the empty set.

To solve a compound inequality, you look for numbers that satisfy both conditions at once—the intersection of the two sets. One condition says x is at most 2, and the other says x is at least 5. Numbers that are at most 2 lie to the left of or at 2 on the number line, while numbers that are at least 5 lie to the right of or at 5. There is no number that can be both at most 2 and at least 5 simultaneously, so the two regions do not overlap. On the number line, there’s a gap between 2 and 5 where neither condition holds. Therefore, no real number satisfies both requirements, and the solution set is the empty set.