Given the equation:
[tex]\frac{x-8a}{6}=3a-2x[/tex]To solve for x, first we move the 6 to the other side of the equation:
[tex]\begin{gathered} \frac{x-8a}{6}=3a-2x \\ \Rightarrow x-8a=(3a-2x)\cdot6 \end{gathered}[/tex]Since the 6 was dividing, we pass it to the other side multiplying. Now we apply the distributive property and move the term -8a to the other side:
[tex]\begin{gathered} x-8a=(3a-2x)\cdot6 \\ \Rightarrow x-8a=18a-12x \\ \Rightarrow x=18a-12x+8a \\ \end{gathered}[/tex]Finally, we move the -12 to the other side with its sign changed:
[tex]\begin{gathered} x+12x=18a+8a=26a \\ \Rightarrow13x=26a \\ \Rightarrow x=\frac{26}{13}a=2a \\ x=2a \end{gathered}[/tex]therefore, x=2a
