Answer:
(-infinity, 0)
(0, 4]
[30, infinity)
Step-by-step explanation:
The inequality seems a little weird since it doesn't reflect the formula for speed accurately. The right inequality should be:
average speed >= 24
(first half speed + second half speed)/2 >= 24
(x+ (x-10))/2 >= 24
x-5>=24
x>= 29
In this case, the answer should be only [30, infinity)
If I solve the inequality given by the problems, the result will be:
1/x + 1/ (x-10) >= 2/24 ---> multiply both side with x(x-10)
x-10 + x >= (2x^2-20x)/24 ---> move /24 to left side
48x-240 >= 2x^2-20x ---> move all left side to right side
0>=2x^2 -68x+240 ---> divide both side by 2
0>=x^2 - 34x +120
0>=x^2-30x -4x+120
x(x-30) -4 (x-30)
(x-4) (x-30)
x1=4 x2=30
Since the coefficient of x^2 is positive so only area between two result is negative.
The answer will be
x1= (-infinity, 4]
x1= (-infinity, 0) , (0, 4]
x2= [30, infinity)
