Question

The graph of which of the following inequalities has open circles on -8 and 2 with a line segment between them

A. |x + 3| < -5
B. |x + 8| < 2
C. |x + 3| < 5

Answer 1

A. Can NOT be true since the absolute value will be greater than 0.
B. Does NOT work with the solutions -8 and 2.
C.√ Correct
|-8+3| = 5
|2+3| = 5

Answer 2

Option C is correct answer.

Explanation:

since -8 and 2 are end points with open circle therefore

If l x -a l < R

means -R< x-a< R

-R+a<x <a+R

Comparing it with -8<x<2 gives

a-R= -8

a+R= 2

Adding both ,we get 2a = -6 which equals a =-3

plugging the value a =-3 in equation a+R=2

-3+R=2 gives R =5

therefore the inequality is lx-(-3) l < 5

on simplifying we get

l x+3< 5

Option C is the correct answer