For what range of values of x is 12 1 2 x + 14 1 4 > 13 1 3 x + 12 1 2 ?

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

Answer Details

$\frac{1}{2}$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 > $\frac{3}{2}$