Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Discover a wealth of knowledge from professionals across various disciplines on our user-friendly Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

On the number line above, if x is a number that lies between a and a + 10, which of the following must betrue?lx - al > 5lx - a -51 < 5lx - a - 101 < 5lx - a + 101 < 5

Sagot :

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