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


Question

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

Options

A) x < \(\frac{3}{2}\)

B) x > \(\frac{3}{2}\)

C) x < -\(\frac{3}{2}\)

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

The correct answer is 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 > \(\frac{3}{2}\)

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Dicussion (1)

  • \(\frac{1}{2}\)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 > \(\frac{3}{2}\)

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