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16 votes
16 votes
I need help with my homework can u walk me through this problem . Question 2

I need help with my homework can u walk me through this problem . Question 2-example-1
User Nbsp
by
2.3k points

1 Answer

26 votes
26 votes

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.

User Ngulam
by
2.7k points
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