Question

Solve the inequality in terms of intervals and illustrate the solution set on the real number line. (x − 1)(x − 8) > 0

Answer 1

Answer:

The solution set of the given inequality is (-∞,1) ∪ (8,∞).

Step-by-step explanation:

The given inequality is

$(x -1)(x -8) > 0$

The related equation is

$(x -1)(x -8)=0$

$x=1,8$

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,∞).