Question 40338
Okay from
48 ≥ 4x(x-1)
let's divide y four first and get
12 ≥ x(x-1)
now expand and rearrange the terms...
x^2 - x - 12 ≤ 0
now factor
(x - 4)(x + 3) ≤ 0
now go to a number line and make solid points at x = 4 and at x = -3
These are your critical points...
Now test any point within each of the three regions we have effectively split the number line into to see if they make the inequality true...
So let's try x = -4 ==> nope that's false
Let's try x = 0 ==> ahh, that works
Now try x = 5 ==> nope false again
So your answer is in between -3 and 4 and we express it as
-3 ≤ x ≤ 4
This is my 1000th solved problem on algebra.com!