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On a number line, point B is at a distance of 5 from point C, and point D is at a distance of 7 from point C.
What is the distance from point B to point D? Please help
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Case 1. The points B and D are on one side from C (let say, both B and D are to the left from C).
Then |B-D| = |7-5| = 2. The distance between B and D is 2 units.
Case 2. The points B and D are on one side from C (let say, both B and D are to the right from C).
Then |B-D| = |7-5| = 2. The distance between B and D is 2 units. Same as Case 1.
Case 3. The points B and D are on different sides from C (let say, B is on the left side, while D is on the right side from C).
Then |B-D| = |7+5| = 12. The distance between B and D is 12 units.
Case 4. The points B and D are on different sides from C (let say, B is on the right side, while D is on the left side from C).
Then the distance |B-D| = |7+5| = 12. The distance between B and D is 12 units. Same as Case 3.
5. There are no other cases.
Answer. There are two solutions and exactly two possibilities: |B-D| = 2 or 12.