Bunuel wrote:

Which of the following inequalities is an algebraic expression for the graph shown? (-3 and 4 are not included in the range)

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

B. \(|x - \frac{1}{2}| > \frac{7}{2}\)

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

D. \(|x - \frac{1}{2}| \geq \frac{7}{2}\)

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

Attachment:

2018-04-01_2151.png

Easiest way i think is by inputting values

input 0

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

PassB. \(|x - \frac{1}{2}| > \frac{7}{2}\)

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

PassD. \(|x - \frac{1}{2}| \geq \frac{7}{2}\)

FailsFails as -3 is not in the range and this option gives RHS = LHS at -3.

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

PassInput -3 in A, C and E

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

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

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

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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