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what is the solution to {x - 6} _> 5?
A. 1 _< x _< 11
B. -11 _< x _< 1
C. x _> 11 or x _< 1
D. x _> 1 or x _< -11



Answer :

The solution to the inequality |x - 6| ≥ 5 is  x ≥ 11 or x ≤ 1. Option C. is the answer

How to find the solution to an absolute inequality equation?

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given: the absolute inequality equation  |x - 6| ≥ 5

|x - 6| ≥ 5

x - 6 ≥ 5

x ≥ 6+5

x ≥ 11

  OR      

   

-(x - 6) ≥ 5

-x + 6 ≥ 5

-x≥ 5-6

-x ≥ -1

x ≤ 1

Thus, the solution is x ≥ 11 or x ≤ 1

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