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