∣x−5∣>11

To find the solution to the inequality ∣x−5∣>11, we can break it down into two separate inequalities:

1. x − 5 > 11
Solving for x:
add 5 to both sides: x > 16

2. -(x − 5) > 11 (Note: when removing the absolute value, the inequality changes direction)
Distribute the negative sign: -x + 5 > 11
Subtract 5 from both sides: -x > 6
Divide both sides by -1 (remember that dividing by a negative number flips the inequality direction): x < -6

Therefore, the solution to the inequality ∣x−5∣>11 is x < -6 or x > 16.