from graph we can get -3<x<4

with option 1 --> -7/2<x-1/2<7/2 solving -3<x<4

hence option A

Easiest way i think is by inputting values
input 0

A. \(|x - \frac{1}{2}| < \frac{7}{2}\)
Pass
B. \(|x - \frac{1}{2}| > \frac{7}{2}\)
Fails
C. \(|x - \frac{1}{2}| \leq \frac{7}{2}\)
Pass
D. \(|x - \frac{1}{2}| \geq \frac{7}{2}\)
Fails
Fails as -3 is not in the range and this option gives RHS = LHS at -3.
E. \(|2x - \frac{1}{2}| < \frac{7}{2}\)
Pass

Input -3 in A, C and E

A. \(|x - \frac{1}{2}| < \frac{7}{2}\)
Pass

C. \(|x - \frac{1}{2}| \leq \frac{7}{2}\)
Fails

E. \(|2x - \frac{1}{2}| < \frac{7}{2}\)
Fails
\(|2*-3 - \frac{1}{2}| = |-6 - \frac{1}{2} | = |\frac{-13}{2}| = \frac{13}{2}which is greater than \frac{7}{2}\) proving the option wrong.

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