Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2 - Page 362: 56

$x=7$

$2x-\frac{2x}{7}=\frac{x}{2}+\frac{17}{2}\\\frac{28x}{14}-\frac{4x}{14}=\frac{7x}{14}+\frac{119}{14}\\\frac{17x}{14}=\frac{119}{14}\\17x=119\\x=7$ Check by plugging it in into the original equation: $2(7)-\frac{2\cdot7}{7}=12$. $\frac{7}{2}+\frac{17}{2}=12$. The two sides are equal, thus it is a good solution.