The locus of points P on the number line such that the distance between P and the point 2 is between 1 and 7 inclusive, is:
- P ≤ 1 or P ≥ 3
- 1 ≤ P ≤ 3
- -5 ≤ P ≤ 9
- -5 ≤ P ≤ 1 or 3 ≤ P ≤ 9
- -6 ≤ P ≤ 1 or 3 ≤ P ≤ 10
Draw it!
So (d).
Or translate it: 1 ≤ |P – 2| ≤ 7
We have two cases: P – 2 > 0 and P – 2 < 0
Case I: P – 2 > 0 and 1 ≤ P – 2 ≤ 7 → P > 2 and 3 ≤ P ≤ 9
Case II: P – 2 < 0 (so 2 - P > 0) and 1 ≤ 2 – P ≤ 7 → P < 2 and -1 ≤ -P ≤ 5
→ P < 2 and 1 ≥ P ≥ -5
So the answer is (d).