Solve $ \frac{2 x+1}{3 x-2}=1\frac{1}{4} $.

Given:

\( \frac{2 x+1}{3 x-2}=1\frac{1}{4} \).
To do:
We have to solve for $x$. 

Solution:

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

\( \frac{2 x+1}{3 x-2}=\frac{1\times4+1}{4} \)

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

$4(2x+1)=5(3x-2)$

$8x+4=15x-10$

$15x-8x=4+10$

$7x=14$

$x=\frac{14}{7}$

$x=2$

The value of $x$ is $2$.