Respuesta :
Given :
[tex]\: {\qquad \sf \dfrac{4}{6} x + \dfrac{10}{4} = - \dfrac{6}{8}x - 10 }[/tex]
⠀
To Find :
- The value of x.
⠀
Solution :
[tex] {\qquad \sf \dashrightarrow \: \dfrac{4}{6} x + \dfrac{10}{4} = - \dfrac{6}{8}x - 10 }[/tex]
⠀
Subtracting [tex] \sf \: \dfrac{10}{4} [/tex] from both sides :
[tex] {\qquad \sf \dashrightarrow \: \dfrac{4}{6} x \: \: \cancel{+ \dfrac{10}{4}} \: \: \cancel{- \dfrac{10}{4}} = - \dfrac{6}{8}x - 10 - \dfrac{10}{4} }[/tex]
⠀
Adding [tex] \sf \dfrac{6}{8} x[/tex] to both sides :
[tex]{\qquad \sf \dashrightarrow \: \dfrac{4}{6} x + \dfrac{6}{8}x = \cancel{- \dfrac{6}{8}x } \: \: \cancel {+ \: \dfrac{6}{8}x} - 10 - \dfrac{10}{4} }[/tex]
[tex]{\qquad \sf \dashrightarrow \dfrac{4}{6} x + \dfrac{6}{8}x = - 10 - \dfrac{10}{4}}[/tex]
⠀
Adding the like terms :
[tex]{\qquad \sf \dashrightarrow \dfrac{32x + 36x}{24} = \dfrac{ - 40 - 10}{4} }[/tex]
[tex]{\qquad \sf \dashrightarrow \dfrac{68x}{24} = \dfrac{ - 50}{4} }[/tex]
[tex]{\qquad \sf \dashrightarrow \dfrac{34x}{12} = \dfrac{ - 25}{2} }[/tex]
⠀
By doing cross multiplication we get :
[tex]{\qquad \sf \dashrightarrow {68x} = - 300 }[/tex]
[tex]{\qquad \sf \dashrightarrow {x} = \dfrac{ - 300}{68} }[/tex]
[tex]{\qquad \bf \dashrightarrow {x} = \dfrac{ - 75}{17} }[/tex]
