Let's solve the inequality [tex]\(|x - 6| \geq 5\)[/tex].
The absolute value inequality [tex]\(|x - 6| \geq 5\)[/tex] can be split into two separate inequalities:
[tex]\[ x - 6 \geq 5 \][/tex]
and
[tex]\[ x - 6 \leq -5 \][/tex]
### Solving the First Inequality
[tex]\[ x - 6 \geq 5 \][/tex]
Add 6 to both sides:
[tex]\[ x \geq 11 \][/tex]
### Solving the Second Inequality
[tex]\[ x - 6 \leq -5 \][/tex]
Add 6 to both sides:
[tex]\[ x \leq 1 \][/tex]
### Combining the Results
From the inequalities, we have:
[tex]\[ x \geq 11 \][/tex]
or
[tex]\[ x \leq 1 \][/tex]
Therefore, the solution to the inequality [tex]\(|x - 6| \geq 5\)[/tex] is:
[tex]\[ x \geq 11 \text{ or } x \leq 1 \][/tex]
Hence, the correct answer is:
C. [tex]\( x \geq 11 \)[/tex] or [tex]\( x \leq 1 \)[/tex]
