The distance d between two villages east more than 18 KM but not more than 23KM. which of these inequalities represents the statements?

Analyze the question

The distance d is described by two conditions:

1. "More than 18 km" means d is greater than 18, written d > 18. It does not include 18.
2. "Not more than 23 km" means d cannot go above 23, written d ≤ 23. It does include 23.

Concept

• "More than" means strictly greater (>).
• "Not more than" means less than or equal to (≤).
• "At least" means ≥, and "less than" means <.

Solution

Combine the two conditions:

• d > 18
• d ≤ 23

Together: 18 < d ≤ 23

Check against the options

• A. 18 ≤ d ≤ 23: wrong, because it includes 18.
• B. 18 < d < 23: wrong, because it excludes 23, but "not more than 23" allows exactly 23.
• C. 18 ≤ d < 23: wrong, because it includes 18 and excludes 23, the opposite of what is needed.
• D. 18 < d ≤ 23: correct, because it excludes 18 and includes 23.

Exam tip

Translate each phrase on its own.

• "More than" or "less than" gives a strict sign (< or >).
• "Not more than" or "not less than" gives a sign with "or equal to" (≤ or ≥).

"Not more than 23" means 23 is the largest allowed value, so 23 itself is included.