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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