For what range of values of x is \(\frac{1}{2}\)x + \(\frac{1}{4}\) > \(\frac{1}{3}\)x + \(\frac{1}{2}\)?
A. x < \(\frac{3}{2}\) B. x > \(\frac{3}{2}\) C. x < -\(\frac{3}{2}\) D. x > -\(\frac{3}{2}\)
Correct Answer: B
Explanation
\(\frac{1}{2}\)x + \(\frac{1}{4}\) > \(\frac{1}{3}\)x + \(\frac{1}{2}\) Multiply through by through by the LCM of 2, 3 and 4 12 x \(\frac{1}{2}\)x + 12 x \(\frac{1}{4}\) > 12 x \(\frac{1}{3}\)x + 12 x \(\frac{1}{2}\) 6x + 3 > 4x + 6 6x - 4x > 6 - 3 2x > 3 \(\frac{2x}{2}\) > \(\frac{3}{2}\) x > \(\frac{3}{2}\)
