1.\(\frac{x}2-\frac{1}5=\frac{x}3+\frac{1}4\)

We have, \(\frac{x}2-\frac{1}5=\frac{x}3+\frac{1}4\)
LCM of denominators 2,5,3 and 4 is 60

So we have \(\frac{x}2×60-\frac{1}5×60=\frac{x}3×60+\frac{1}4×60\quad \)[Multiplying both the sides by 60 ]

\(\Rightarrow 30x -12 =20x +15\)

\(\Rightarrow 30x -20x =15+12 \)[Transposing 20x to LHS and 12 to RHS]

\(\Rightarrow 10x =27\)

\(\Rightarrow x =\frac{27}{10}\)[Dividing by 10 on both the sides]