|1-4k| ≥ -11

Question

Solve

Answer 1

1-4k >= -11 and -1+4k >=-11
-4k >= -12 _and ___4k>=-10
4 k <= 12 __and_____k>=-2.5
k <= 3
note
arrow
reverse
when
signs
changed

so in the end between -3and +3
-2.5 <= k <= 3

Answer 2

This is a trick question.

|u| is always positive, so

|1-4k| ≥ -11

for any value of k.

Damon's solution is correct, but it should read

k >= -2.5 OR k <= 3

So, any value of k will work.