If x is any integer from -6 to 2 inclusive, how many

My solution:

First note that there are 9 integers from -6 to 2 inclusive.

Given: 2 - |x³ + 10x² - 24x| < 2
Add |x³ + 10x² - 24x| to both sides: 2 < 2 + |x³ + 10x² - 24x|
Subtract 2 from both sides to get: 0 < |x³ + 10x² - 24x|
Now let's apply some number sense.
We know that the absolute value of something will always be greater than or equal to zero. So the ONLY values that DON'T satisfy the inequality 0 < |x³ + 10x² - 24x| will be those values where |x³ + 10x² - 24x| = 0
In other words, x³ + 10x² - 24x = 0
Factor to get: x(x² + 10x - 24) = 0
Factor more: x(x + 12)(x - 2) = 0
Solve to get: x = 0, or x = -12 or x = 2
So, x = 0, or x = -12 or x = 2 are the ONLY values of x that DON'T satisfy the inequality 0 < |x³ + 10x² - 24x|
Since x = -12 is not within the given range of values (-6 to 2 inclusive), we need only consider the 2 values (x = 0 and x = 2)
So, the number of integer values that DO satisfy the inequality = 9 - 2 = 7

Answer: C