Question

$\frac{1}{4}x+ \frac{1}{2}= \frac{1}{4}x- \frac{1}{2}$

Answer 1

$\dfrac{1}{4}x + \dfrac{1}{2} = \dfrac{1}{4}x- \dfrac{1}{2}$ 

$\text{Cancel 1/4x on both sides}$ 

$\dfrac{1}{2}=-\dfrac{1}{2}$ 

$\text{There is no solution}$

Answer 2

1/4x + 2/4 = 1/4x - 2/4
1/4x - 1/4x = -2/4 - 2/4
0x = 0
x = 0