#### Answer

$\frac{77}{15}$

#### Work Step by Step

Multiply 12 (the LCD of the fractions) on both sides of the equation to obtain:
$\require{cancel}
12(\frac{3x+1}{3}-\frac{13}{2}) = 12(\frac{1-x}{4})
\\12(\frac{3x+1}{3})-12(\frac{13}{2}) = \cancel{12}3(\frac{1-x}{\cancel{4}})
\\\cancel{12}4(\frac{3x+1}{\cancel{3}})-\cancel{12}6(\frac{13}{\cancel{2}}) = 3(1-x)
\\4(3x+1)-6(13)=3-3x
\\12x+4-78=3-3x
\\12x-74=3-3x$
Add $3x$ on both sides of the equation to obtain:
$15x-74=3$
Add $74$ on both sides of the equation to obtain:
$15x=77$
Divide 15 on both sides of the equation to obtain:
$x=\frac{77}{15}$