We have the following inequality,
[tex]|\frac{x}{4}|+1\le2[/tex]
By subtracting 1 to both sides, we have
[tex]|\frac{x}{4}|\le1[/tex]
From the absolute value properties, this inequality can solved in 2 cases:
[tex]\begin{gathered} i)\frac{x}{4}\le1 \\ ii)\frac{x}{4}\ge-1 \end{gathered}[/tex]
Case i).
By multiplying both sides by 4, we have
[tex]x\le4[/tex]
Case ii)
Similarly, by multiplying both sides by 4, we get
[tex]x\ge-4[/tex]
Therefore, the answer is the intersection of both results, that is,
[tex]-4\le x\le4[/tex]
Then, the answer is option A.
