Answer
$x=1$
Work Step by Step
$\frac{x+1}{4} = \frac{1}{6} + \frac{2-x}{3}$
Take LCD at the right hand side
$\frac{x+1}{4} = \frac{1+2(2-x)}{6}$
$\frac{x+1}{4} = \frac{1+4-2x}{6}$
$\frac{x+1}{4} = \frac{5-2x}{6}$
Multiply both sides by 24 to clear fractions.
$24(\frac{x+1}{4}) = 24(\frac{5-2x}{6})$
$6(x+1)= 4(5-2x)$
$6x+6= 20-8x$
Combine like terms.
$6x+8x= 20-6$
$14x = 14$
$ x = \frac{14}{14}$
$x=1$
