SOLUTION: If 8 less than the product of a number and - 3 is greater than 7, which of the following could be that number? Select one: A. - 5 B. 5 C. 6 D. - 6

We put in some parentheses and brackets:

We start with simplifying this: (the product of a number and -3) 
That simplifies to -3x.

Then the problem becomes: 

Then we simplify this:  [8 less than -3x]
That simplifies to -3x-8 because to make -3x  less we start with the thing we
want to make less, which is -3x, and then we subtract 8 from it, so we get
-3x-8.

Then the problem becomes: 

Now the problem is

We solve that inequality:

-3x-8 > 7

We add +8 to both sides and get

-3x > 15

Then we divide both sides by -3, remembering that when we divide an
inequality by a negative number, we must flip the inequality symbol:

 x < -5.

If we put A, B, C, and D on a number line we have

-o---o---------------------------------------o---o---
-6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6  7     

and we see that only -6 is less than -5.

So the correct answer is D.

Edwin