Question

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

Answer 1

`-6\leq x\leq 16`

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!