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

For what range of values of x is (frac{1}{2})x + (frac{1}{4}) > (frac{1}{3})x + (frac{1}{2})?
  • A.
    x
  • B.
    x > (frac{3}{2})
  • C.
    x
  • D.
    x > -(frac{3}{2})
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})

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