Solving:
[tex] \frac{3+4x}{2} + \frac{5-x}{3} = \frac{29}{6} [/tex]
Make the Least Common Multiple (2,3,6)
[tex]2,3,6\:|2[/tex]
[tex]1,3,3\:|3[/tex]
[tex]1,1,1\:|\underline{2*3=6}[/tex]
Replace denominators and resolve:
[tex] \frac{3+4x}{2} + \frac{5-x}{3} = \frac{29}{6} [/tex]
[tex] \frac{3(3+4x)}{6} + \frac{2(5-x)}{6} = \frac{29}{6} [/tex]
Cancel the dominators
[tex] \frac{3(3+4x)}{\diagup\!\!\!\!6} + \frac{2(5-x)}{\diagup\!\!\!\!6} = \frac{29}{\diagup\!\!\!\!6} [/tex]
[tex]3(3+4x) + 2(5-x) = 29[/tex]
[tex]9 + 12x + 10 - 2x = 29[/tex]
[tex]12x - 2x = 29 - 9 - 10[/tex]
[tex]10x = 20 - 10[/tex]
[tex]10x = 10[/tex]
[tex]x = \frac{10}{10} [/tex]
[tex]\boxed{\boxed{x = 1}}\end{array}}\qquad\quad\checkmark[/tex]
