If 8 less than the product of a number and - 3 is greater than 7, which of the
following could be that number?
We put in some parentheses and brackets:
If [8 less than (the product of a number and -3)] is greater than 7, which of
the following could be that number?
We start with simplifying this: (the product of a number and -3)
That simplifies to -3x.
Then the problem becomes:
If [8 less than -3x] is greater than 7, which of the following could be that
number?
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:
If [-3x-8] is greater than 7, which of the following could be that number?
Now the problem is
If [-3x-8] > 7, which of the following could be that number?
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