Question

Solve the following inequality algebraically. ∣x−5∣≤11

Answer 1

Answer:

$-6\leq x\leq 16$

Step-by-step explanation:

So we have the inequality:

$|x-5|\leq 11$

Definition of Absolute Value:

$x-5\leq 11\text{ or } x-5\geq -11$

Note that the sign is flipped in the second case because we multiplied by a negative.

Add 5 to both sides to both equations:

$x\leq 16\text{ or } x\geq -6$

Merge:

$-6\leq x\leq 16$

And we're done!