Question

What is the solution for x2 –18x < –77? x < –11 or x > 7 x < –7 or x > 11 –11 < x < 7 7 < x < 11

Answer 1

Step 1:

Write the inequality

`x^2\text{ - 18x < - 77}`

Step 2:

`\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}`

Final answer

7 < x < 11