Show that for any positive number $\varepsilon$ we can find a positive number $\delta$ such that the statement below is satisfied.
-15x - 125 is less than $\varepsilon$ away from 130 whenever $\mathrm{x}$ is less than $\delta$ away from - 17 .
A) $\delta=\frac{\varepsilon}{-15}$

B) $\delta=\frac{\varepsilon}{-17}$

C) $\delta=\frac{\varepsilon}{17}$

D) $\delta=\frac{\varepsilon}{15}$

Question

Show that for any positive number $\varepsilon$ we can find a positive number $\delta$ such that the statement below is satisfied.
-15x - 125 is less than $\varepsilon$ away from 130 whenever $\mathrm{x}$ is less than $\delta$ away from - 17 .
A) $\delta=\frac{\varepsilon}{-15}$

B) $\delta=\frac{\varepsilon}{-17}$

C) $\delta=\frac{\varepsilon}{17}$

D) $\delta=\frac{\varepsilon}{15}$

Quizplus · Accepted Answer

To satisfy the condition, we need $|15x - 125 - 130| < \varepsilon$, which simplifies to $|15x - 255| < \varepsilon$. This implies $|15(x + 17)| < \varepsilon$, leading to $|x + 17| < \frac{\varepsilon}{15}$. Therefore, $\delta = \frac{\varepsilon}{15}$.

Show That for Any Positive Number ε\varepsilonε We Can Find a Positive Number

Show That for Any Positive Number $\varepsilon$ We Can Find a Positive Number