See figure and explanations below.
Work Step by Step
As $ c-a=0.2409, b-c=0.2391$; we choose $0\lt\delta\leq 0.2391$, so that for any $ x, 0\lt |x-c|\lt\delta $, we have $ a\lt x\lt b $ as can be seen in the figure.
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.