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 + $$\frac{1}{2}$$?...

### 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 > -$$\frac{3}{2}$$

### 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 > $$\frac{3}{2}$$

## 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 > $$\frac{3}{2}$$