Answer:
[tex] -17x = 234 [/tex]
Step-by-step explanation:
[tex] \dfrac{2x}{3} - \dfrac{5x}{9} - \dfrac{x}{6} - \dfrac{5x}{12} = \dfrac{13}{2} [/tex]
First, we find the LCD. It is 36. Multiply both sides by 36.
[tex] 36\left(\dfrac{2x}{3} - \dfrac{5x}{9} - \dfrac{x}{6} - \dfrac{5x}{12}\right) = 36\left(\dfrac{13}{2}\right) [/tex]
[tex] 36\left(\dfrac{2x}{3}\right) - 36\left(\dfrac{5x}{9}\right) - 36\left(\dfrac{x}{6}\right) - 36\left(\dfrac{5x}{12}\right) = \dfrac{36}{2}(13) [/tex]
[tex] \dfrac{36}{3}(2x) - \dfrac{36}{9}(5x) - \dfrac{36}{6}(x) - \dfrac{36}{12}(5x) = 18(13) [/tex]
[tex] 12(2x) - 4(5x) - 6(x) - 3(5x) = 234 [/tex]
[tex] 24x - 20x - 6x - 15x = 234 [/tex]
[tex] -17x = 234 [/tex]
