[tex]\dfrac{2}{3}\left(x+\dfrac{1}{2}\right)-\dfrac{1}{4}=\dfrac{5}{2}\qquad|\text{use distributive property}\\\\\dfrac{2}{3}x+\dfrac{2}{3}\cdot\dfrac{1}{2}-\dfrac{1}{4}=\dfrac{5}{2}\\\\\dfrac{2}{3}x+\dfrac{1}{3}-\dfrac{1}{4}=\dfrac{5}{2}\qquad|\text{multiply both sides by LCM(2,\ 3,\ 4)=12}\\\\12\cdot\dfrac{2}{3}x+12\cdot\dfrac{1}{3}-12\cdot\dfrac{1}{4}=12\cdot\dfrac{5}{2}\\\\4\cdot2x+4-3=6\cdot5\\\\8x+1=30\qquad|\text{subtract 1 from both sides}\\\\8x=29\qquad|\text{divide both sides by 8}\\\\x=\dfrac{29}{8}[/tex]
