[tex]|1-4k|\ge-11[/tex]
This implies that
[tex]\begin{gathered} 1-4k\ge-11 \\ or \\ 1-4k\leq11 \end{gathered}[/tex][tex]\begin{gathered} \text{If 1-4k}\ge-11 \\ -4k\text{ }\ge-11-1 \\ -4k\ge-12 \\ k\leq3 \end{gathered}[/tex][tex]\begin{gathered} \text{If 1-4k}\leq11 \\ -4k\text{ }\leq11-1 \\ -4k\leq10 \\ k\ge-\frac{5}{2} \end{gathered}[/tex]
Combining both of them
[tex]-\frac{5}{2}\leq k\leq3[/tex]
Drawing the inequality line yields
