1 Answer

Abdul Rahman A Samad · Answer 1 · 2023-07-21T22:35:35+0000

We have the following inequality,

$|(x)/(4)|+1\le2$

By subtracting 1 to both sides, we have

$|(x)/(4)|\le1$

From the absolute value properties, this inequality can solved in 2 cases:

$\begin{gathered} i)(x)/(4)\le1 \\ ii)(x)/(4)\ge-1 \end{gathered}$

Case i).

By multiplying both sides by 4, we have

$x\le4$

Case ii)

Similarly, by multiplying both sides by 4, we get

$x\ge-4$

Therefore, the answer is the intersection of both results, that is,

$-4\le x\le4$

Then, the answer is option A.

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