Question

Find the root of the equation 6x−5/7 = 2x −1/3 +2

Answer 1

Given the initial expression

`\begin{gathered} (6x-5)/(7)=(2x-1)/(3)+2 \\ \Leftrightarrow(6x-5)/(7)-(2x-1)/(3)-2=0 \end{gathered}`

Solving for x,

`\begin{gathered} \Rightarrow(6x-5)/(7)-((2x-1))/(3)=2 \\ \Rightarrow(6x)/(7)-(5)/(7)-(2x)/(3)+(1)/(3)=2 \\ \Rightarrow(6x)/(7)-(2x)/(3)=2+(5)/(7)-(1)/(3) \\ \Rightarrow(4x)/(21)=(50)/(21) \\ \Rightarrow x=(50)/(4)=(25)/(2) \\ \Rightarrow x=(25)/(2) \end{gathered}`

Thus, the answer is x=25/2.

x=25/2 is the root of the equation

`(6x-5)/(7)-(2x-1)/(3)-2=0`