Answer:
[tex]-6\leq x\leq 16[/tex]
Step-by-step explanation:
So we have the inequality:
[tex]|x-5|\leq 11[/tex]
Definition of Absolute Value:
[tex]x-5\leq 11\text{ or } x-5\geq -11[/tex]
Note that the sign is flipped in the second case because we multiplied by a negative.
Add 5 to both sides to both equations:
[tex]x\leq 16\text{ or } x\geq -6[/tex]
Merge:
[tex]-6\leq x\leq 16[/tex]
And we're done!
