We are given the following inequalities:
[tex]\begin{gathered} 3x-5<-14,(1)\text{ or} \\ 2x-1>7,(2) \end{gathered}[/tex]First, we will solve for inequality 1. To do that we will add 5 to both sides:
[tex]3x-5+5<-14+5[/tex]Solving the operations:
[tex]3x<-9[/tex]Now we divide both sides by 3:
[tex]\frac{3x}{3}<-\frac{9}{3}[/tex]Solving the operations:
[tex]x<-3[/tex]Now we solve for "x" in inequality (2). To do this we will add 1 to both sides:
[tex]2x-1+1>7+1[/tex]Solving the operations:
[tex]2x>8[/tex]Now we divide both sides by 2:
[tex]\frac{2x}{2}>\frac{8}{2}[/tex]Solving the operations:
[tex]x>4[/tex]Therefore, the solution to the system is:
[tex]x<-3\text{ or x > 4}[/tex]