Solution
Step 1:
Write the inequality
[tex]x^2\text{ - 18x < - 77}[/tex]Step 2:
[tex]\begin{gathered} x^2\text{ - 18x + 77 < 0} \\ x^2\text{ - 7x - 11x + 77 < 0} \\ x(x\text{ - 7\rparen -11\lparen x - 7\rparen < 0} \\ (x\text{ - 11\rparen\lparen x - 7\rparen < 0} \\ \text{x - 11 < 0 , x - 7 > 0} \\ \text{x < 11 , x > 7} \end{gathered}[/tex]Final answer
7 < x < 11