Find the largest possible value of $\delta$ that makes the following statement true: "If $0

Question

Find the largest possible value of $\delta$ that makes the following statement true: "If $0 < | x - 1 | < \delta$ then $| ( 2 x + 3 ) - 5 | < 0.2 "$
A) 0.2
B) 0.05
C) 0.1
D) None of these

Quizplus · Accepted Answer

To solve for $\delta$, we start by simplifying the inequality $| (2x + 3) - 5 | < 0.2$ to $|2x - 2| < 0.2$, which simplifies further to $|2(x - 1)| < 0.2$. Dividing both sides by 2 gives $|x - 1| < 0.1$. Therefore, the largest possible value of $\delta$ is 0.1.

Find the Largest Possible Value Of δ\deltaδ That Makes the Following Statement True: "If

Find the Largest Possible Value Of $\delta$ That Makes the Following Statement True: "If