Question

Given two points A,B with the coordinates: A = x, B = 7. Express the following statement as an inequality that involves the absolute value symbol: "d(A,B) is greater than 1".​

Answer 1

Given : Two points A,B with the coordinates: A = x, B = 7.

d(A,B) is greater than 1"

To Find : Express  as an inequality

Solution:

d (A , B)  = B - A   if B ≥ A  

              or A - B  if A > B

or

or d (A , B) =  | B - A |

"d(A,B) is greater than 1"

=> | B - A |  > 1

B = 7  and A = x

=> | 7 - x |  > 1

Required inequality  is   | 7 - x |  > 1

Additional info :

7 - x  > 1  => x <  6

7 - x  < - 1   => x > 8

x ∈  R - [6 , 8]    or  x ∈ (-∞ , 6) U (8 , ∞)

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