Answer:
x≤-3 2 ≤x<7
Step-by-step explanation:
(x^2+x-6) /(x-7) ≤0
Factor the numerator
(x+3)(x-2) / (x-7)≤0
Critical points are
X =-3 X =2 X=7
We need to check the values when
x≤3 -3 ≤ x≤2 2 ≤x<7 x>7
(x cannot be 7 because then the denominator is zero)
and see when it is less than 0
Substitute a value in and see if factor is positive or negative
x≤-3
(negative)(negative) / (negative) = negative
-3 ≤x≤2
(positive)(negative) / (negative) = positive this range does not work
2 ≤x<7
(positive)(positive) / (negative) = negative
x>7
(positive)(positive) / (positive)
