Question

-

Answer 1

It is important to know the definition of absolute value.
|x|=x if x>0 or if x=0
|x|=-x if x<0
-- x>0 think we are looking to the right of 0
--x<0 think we are looking to the left of 0

So
|x-8|=x-8 if x-8>0 or if x-8=0
|x-8|=-(x-8) if x-8<0

Answer 2

Your question says you are looking to the left of 8
which means you should be thinking of values less than 8

Answer 3

So which one will you use for |x-8|

Answer 4

the choices are
A) x-8
B -(x-8)

Answer 5

a?

Answer 6

but |x-8|=x-8 if x>8
and |x-8|=-(x-8) if x<8

Answer 7

you could yust mathway.com

Answer 8

you have x is approaches values to the left of 8 not to the right

Answer 9

since x is approaching to the left you have |x-8|=-(x-8)

Answer 10

if you had \[\lim_{x \rightarrow 8^+} \frac{|x-8|}{x-8}=\lim_{x \rightarrow 8^+}\frac{x-8}{x-8}=1\]

but instead of that little + sign thingy you have the - sign thingy

Answer 11

\[\lim_{x \rightarrow 8^-}\frac{|x-8|}{x-8}=...\]
and that - sign thing means you want to look to the left of 8 as you are approaching 8
which means you are looking at values then 8 which means you are looking at x<8
and in the definition I wrote |x-8|=-(x-8) if x<8
also if you don't see that x<8 if x-8<0 then try adding 8 on both sides to solve the inequality

Answer 12

@chris215 are you still confused what to do?

Answer 13

\[\lim_{x \rightarrow 8^-} \frac{|x-8|}{x-8}=\lim_{x \rightarrow 8^-} \frac{-(x-8)}{x-8}=...\]

Answer 14

-1?

Answer 15

yes