Which of the following is the solution

The answer is the second option.

First of all, let's rearrange the inequality by dividing both sides by 4. Since we are dividing by a positive number, we preserve the inequality sign. So, we have

Now, let's focus on what absolute value does in general. The absolute value function takes a number as input, and returns the positive version of that input. In other words, if fed with a positive input , the function will return itself, since it was already positive. On the contrary, a negative output yields the output , to make sure that the output is positive.

So, if you want the absolute value of a number to be greater than or equal to 4, you can either take a positive number greater than or equal to 4, or a negative number smaller than or equal to -4. Let me show a couple of example.

If you choose 17, then you have , which proves that a positive number greater than 4 is a good choice.

Similarly, if you choose -6, then you have , which proves that a negative number smaller than -4 is also a good choice.

Now let's return to our equation: we want

and we just proved that we need the quantity inside the absolute value to be larger than or equal to 4 of less than or equal to -4. In formula, this becomes

or

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