Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2 - Page 362: 58

$x=59$

$\frac{x-2}{3}-4=\frac{x+1}{4}\\\frac{4x-8}{12}-\frac{48}{12}=\frac{3x+3}{12}\\4x-8-48=3x+3\\x=59$ Check by plugging it in into the original equation: $\frac{59-2}{3}-4=15$. $\frac{59+1}{4}=15$. The two sides are equal, thus it is a good solution.