[tex]-\dfrac{17}{6}x+1=\dfrac{7}{6}-\dfrac{5}{2}x\\\\\text{Most people do not like fractions. Well, let's get rid of them.}\\\\\text{Find the common denominator.... It's 6 :)}.\\\\\text{Multiply both sides of the equation by 6:}\\\\6\!\!\!\!\diagup^1\cdot\left(-\dfrac{17}{6\!\!\!\!\diagup_1}x\right)+6\cdot1=6\!\!\!\!\diagup^1\cdot\dfrac{7}{6\!\!\!\!\diagup_1}-6\!\!\!\!\diagup^3\cdot\dfrac{5}{2\!\!\!\!\diagup_1}x\\\\-17x+6=7-3\cdot5x\qquad\text{subtract 6 from both sides}[/tex]
[tex]-17x=1-15x\qquad\text{add 15x to both sides}\\\\-2x=1\qquad\text{divide both sides by (-2)}\\\\\boxed{x=-\dfrac{1}{2}}[/tex]
