Question

Express the fact that x differs from 2 by more than 3 as an inequality involving an absolute value. Solve for x.

Answer 1

Given statement can be written as: |x-2|>3
or -3 > x-2 > 3
Adding 2 each side, we obtain
-3+2 > x-2+2 > 3 + 2
-1>x>5
x < -1 or x > 5
The value of x lies between two intervals: (-infinity, -1) or (5, +infinity)

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