We are given an inequality proble. Our approach is to test our options.
We begin with the second option.
[tex]\begin{gathered} |x-a-5|<5 \\ \text{This translates to:} \\ -5<|x-a-5|<5 \end{gathered}[/tex]We'll solve it in parts and compare to our number line
[tex]\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}[/tex]The range of x is therefore: a < x < 10 + a
SECOND OPTION
