INFORMATION:
We have the next inequality
[tex]x^2-9x<-8[/tex]And we must find its solution
STEP BY STEP EXPLANATION:
To solve it, we must:
1. Move all terms aside
[tex]x^2-9x+8<0[/tex]2. Factor x^2-9x+8
[tex](x-8)(x-1)<0[/tex]3. Solve for x
[tex]x=8\text{ or }x=1[/tex]4. From the values of x, we have these 3 intervals to test
[tex]\begin{gathered} x<1 \\ 18 \end{gathered}[/tex]5. Choose a test point for each interval
For the interval x < 1:
[tex]\begin{gathered} \text{ Using x }=0, \\ 0^2-9(0)<-8 \\ 0<-8 \end{gathered}[/tex]which is false. So, the interval is discarded.
For the interval 1 < x < 8:
[tex]\begin{gathered} \text{ Using x }=2, \\ 2^2-9(2)<-8 \\ -14<-8 \end{gathered}[/tex]which is true. So, the interval is maintained
For the interval x > 8:
[tex]\begin{gathered} \text{ Using x = 9,} \\ 9^2-9(9)<-8 \\ 0<-8 \end{gathered}[/tex]which is false. So, the interval is discarded.
Finally, the solution would be the interval that was maintained: 1 < x < 8.
ANSWER:
C. 1 < x < 8
