Starting with the given equation:
[tex]-2+\sqrt[]{3x-2}=6[/tex]Add 2 to both sides of the equation:
[tex]\begin{gathered} \Rightarrow-2+\sqrt[]{3x-2}+2=6+2 \\ \Rightarrow\sqrt[]{3x-2}=8 \end{gathered}[/tex]Square both sides of the equation:
[tex]\begin{gathered} \Rightarrow(\sqrt[]{3x-2})^2=8^2 \\ \Rightarrow3x-2=64 \end{gathered}[/tex]Add 2 to both sides of the equation:
[tex]\begin{gathered} \Rightarrow3x-2+2=64+2 \\ \Rightarrow3x=66 \end{gathered}[/tex]Divide both sides by 3:
[tex]\begin{gathered} \Rightarrow x=\frac{66}{3} \\ \Rightarrow x=22 \end{gathered}[/tex]Therefore, the solution to the given equation is:
