Answer:
[tex]\{x|x<-\frac{13}{2}\}[/tex]
Explanation:
Given the inequality:
[tex]\frac{11-6x}{5}>10[/tex]
Step 1: Multiply both sides of the inequality by 5.
[tex]\begin{gathered} \frac{11-6x}{5}\times5>10\times5 \\ 11-6x>50 \end{gathered}[/tex]
Step 2: Subtract 11 from both sides.
[tex]\begin{gathered} 11-11-6x>50-11 \\ -6x>39 \end{gathered}[/tex]
Step 3: Divide both sides by -6. Reverse the inequality sign because we are dividing by a negative number.
[tex]\begin{gathered} \frac{-6x}{-6}<\frac{39}{-6} \\ x<-\frac{13}{2} \end{gathered}[/tex]
The solution set of the inequality is therefore:
[tex]\{x|x<-\frac{13}{2}\}[/tex]
The correct choice is B.
