Inequalities

[SaraLove]

Each of the following sets is the solution of an inequality of the form |x-c| < (a symbol that looks like 8 but doesn't have the top part) Find C and (variable that looks like 8)

for (-2, 2)
(0,4)
and a, b)

I'm so sorry for not being specific.

 

[HallsofIvy]

Each of the following sets is the solution of an inequality of the form |x-c| < (a symbol that looks like 8 but doesn't have the top part)

Is it possible that you mean "\(\displaystyle \alpha\)", the Greek letter "alpha": \(\displaystyle |x- c|<\alpha\)?

Find C and (variable that looks like 8)

for (-2, 2)
(0,4)
and a, b)

I'm so sorry for not being specific.

\(\displaystyle |x- c|<\alpha\) is the same as \(\displaystyle -\alpha< x- c< \alpha\) which, adding c to each part, is the same as \(\displaystyle c-\alpha< x< c+ \alpha\).
x lies in an interval with c at the center and extending a distance \(\displaystyle \alpha\) on either side.

So, what is the center point of the interval (-2, 2)? How far does it extend on either side? What is the center point of the interval (0, 4)? How far does it extend on either side? What is the center point (a, b) (I presume you forgot the "(")? How far does it extend on either side?