From the problem, we have an inequality :
[tex]-6x+1<7[/tex]
Subtract 1 to both sides of the equation :
[tex]\begin{gathered} -6x+1-1<7-1 \\ -6x<6 \end{gathered}[/tex]
Divide both sides by -6 :
[tex]\begin{gathered} -6x<6 \\ x<\frac{6}{-6} \\ x<-1 \end{gathered}[/tex]
The solution is x < -1
