Respuesta :
ANSWER
[tex](-\infty,-\frac{1}{6})\cup[6,\infty)[/tex]EXPLANATION
We want to solve the inequality:
[tex]18x-5<-8\text{ or }7x-4\ge38[/tex]Let us solve the first inequality.
First, add 5 to both sides of the inequality:
[tex]\begin{gathered} 18x-5+5<-8+5 \\ \\ 18x<-3 \end{gathered}[/tex]Now, divide both sides of the inequality by 18:
[tex]\begin{gathered} x<\frac{-3}{18} \\ \\ x<-\frac{1}{6} \end{gathered}[/tex]Let us solve the second inequality. Add 4 to both sides of the inequality:
[tex]\begin{gathered} 7x-4+4\ge38+4 \\ \\ 7x\ge42 \end{gathered}[/tex]Now, divide both sides of the inequality by 7:
[tex]\begin{gathered} x\ge\frac{42}{7} \\ \\ x\ge6 \end{gathered}[/tex]Therefore, the solution for x is:
[tex]\begin{gathered} x<-\frac{1}{6}\text{ or }x\ge6 \\ \\ (-\infty,-\frac{1}{6})\cup[6,\infty) \end{gathered}[/tex]