Answer :
Given the inequality:
[tex]4(x-6)-42x<-9(4x+6)-3x[/tex]We can use the distributive property on the parenthesis to get the following:
[tex]\begin{gathered} 4(x-6)-42x<-9(x+6)-3x \\ \Rightarrow4x-24-42x<-9x-54-3x \\ \Rightarrow-24-38x<-39x-54 \end{gathered}[/tex]Now we can move the term -39x to the left and -24 to the right to get the follownig expression:
[tex]\begin{gathered} -24-38x<-39x-54 \\ \Rightarrow39x-38x<-54+24=-30 \\ \Rightarrow x<-30 \end{gathered}[/tex]therefore, the solution of the inequality is x < -30