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

Question

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 $x$,
$0 < | x - c | < \delta \Rightarrow a < x < b \text {. }$
-$a = - 2 , b = 8 , c =$
A) $\delta = 3$
B) $\delta = 4$
C) $\delta = 7$
D) $\delta = 1$

Quizplus · Accepted Answer

The greatest value for $\delta$ is the minimum of the distances from $c$ to $a$ and $b$. In this case, the distance from $c$ to $a$ is $|-2 - 4| = 6$ and the distance from $c$ to $b$ is $|8 - 4| = 4$. Therefore, the greatest value for $\delta$ is $4$.

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

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