Given
[tex]1-4x=\frac{2}{3}(-2+x)[/tex]
Solve for x as shown below
[tex]\begin{gathered} 1-4x=\frac{2}{3}\cdot-2+\frac{2}{3}\cdot x \\ \Rightarrow1-4x=-\frac{4}{3}+\frac{2x}{3} \end{gathered}[/tex]
Therefore, the mistake is in step 1. He did not multiply x by 2/3
