For what range of values of x is \(\frac{1}{2}\)x + \(\frac{1}{4}\) &gt; \(\frac{1}{3}\)x + \(\frac{1}{2}\)?

For what range of values of x is \(\frac{1}{2}\)x + \(\frac{1}{4}\) > \(\frac{1}{3}\)x + \(\frac{1}{2}\)?

Mathematics

JAMB 2010

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 > -\(\frac{3}{2}\)

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Correct Answer: Option 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 > \(\frac{3}{2}\)

There is an explanation video available below.

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