Answer:
The solution set of the given inequality is (-∞,1) ∪ (8,∞).
Step-by-step explanation:
The given inequality is
[tex](x -1)(x -8) > 0[/tex]
The related equation is
[tex](x -1)(x -8)=0[/tex]
[tex]x=1,8[/tex]
Two numbers 1 and 8 divide the number line in three intervals. (-∞,1), (1,8) ,(8,∞).
Intervals check point (x -1)(x -8) > 0 True or False
(-∞,1) 0 (-1)(-8)=8>0 True
(1,8) 2 (2-1)(2-8)=-6>0 False
(8,∞) 9 (9-1)(9-8)=8>0 True
The given inequality is true for (-∞,1) and (8,∞).
Therefore, the solution set of the given inequality is (-∞,1) ∪ (8,∞).
