Given the Interval $( a , b )$ On The $x$ -Axis with the Point

Multiple Choice

Given the interval $( a , b )$ on the $x$ -axis with the point $c$ inside, find the greatest value for $\delta > 0$ such that for all $x$ ,
$0 < | x - c | < \delta \Rightarrow a < x < b \text {. }$
- $$a = \frac { 3 } { 9 } , b = \frac { 8 } { 9 } , c = \frac { 4 } { 9 }$$

A) $\delta = 1$
B) $\delta = \frac { 1 } { 9 }$
C) $\delta = 0$
D) $\delta = \frac { 4 } { 9 }$