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Haolee · Answer 1 · 2023-10-31T02:08:35+0000

We are given an inequality proble. Our approach is to test our options.

We begin with the second option.

$\begin{gathered} |x-a-5|<5 \\ \text{This translates to:} \\ -5<|x-a-5|<5 \end{gathered}$

We'll solve it in parts and compare to our number line

$\begin{gathered} -5<(x-a-5) \\ \text{Adding 5 to both sides gives us:} \\ -5+5On the other hand, we have:[tex]\begin{gathered} (x-a-5)<5 \\ \text{Adding 5 to both sides} \\ x-a<5+5 \\ x-a<10 \\ \text{Adding a to both sides} \\ x<10+a \end{gathered}$

The range of x is therefore: a < x < 10 + a

SECOND OPTION

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