The sum of two negative numbers is always negative, hence, this is the right choice.

As for the other choices:

The product or quotient of two negative numbers is always positive. 

A negative number taken to the power of a positive integer can be either negative or positive depending on whether the exponent is even or odd. \(\displaystyle (-2) ^{2} = 4\), which is positive, and \(\displaystyle (-2) ^{3} = -8\), which is negative.

The difference of negative numbers can be either negative, positive, or zero:

\(\displaystyle -4 - (-5) = -4 + 5 = 1\), but \(\displaystyle -5 - (-4) = -5 + 4 = -1\)

Because \(\displaystyle \dpi{100} \small -3b\) is positive, \(\displaystyle \dpi{100} \small b\) must be negative since the product of two negative numbers is positive.

Because \(\displaystyle \dpi{100} \small ab\) is also positive, \(\displaystyle \dpi{100} \small a\) must also be negative in order to produce a prositive product.

To check you answer, you can try plugging in any negative number for \(\displaystyle \dpi{100} \small a\).

By choosing a random negative number, for example: –4, we can input the number into each choice and see if we come out with another negative number.  When we put –4 in for x, we would have –4 – (–(–4)) or –4 – 4, which is –8.  Plugging in the other options gives a positive answer.  You can try other negative numbers, if needed, to confirm this still works. 

x: –7 – 7= –7 + –7 = –14

y: –7 – (–7) = –7 + 7 = 0

when subtracting a negative number, turn it into an addition problem

Begin by isolating your variable.

Subtract \(\displaystyle x\) from both sides:

\(\displaystyle 16-4x-x=6\), or \(\displaystyle 16-5x=6\)

Next, subtract \(\displaystyle 16\) from both sides:

\(\displaystyle -5x=6-16\), or \(\displaystyle -5x=-10\)

Then, divide both sides by \(\displaystyle -5\):

\(\displaystyle x=\frac{-10}{-5}\)

Recall that division of a negative by a negative gives you a positive, therefore:

\(\displaystyle x=\frac{10}{5}\) or \(\displaystyle x=2\)

The rule for dividing negative numbers is the same as for multiplying negative numbers.  

If both numbers are negative, you will get a positive answer.  

If either number is positive, and the other is negative, you will get a negative answer.  

Therefore:

\(\displaystyle \frac{-288}{-16} = 18\)

To solve, first put the equation in terms of \(\displaystyle x\):

\(\displaystyle -\frac{396}{x} = 12\)

First multiply the x to both sides.

\(\displaystyle 12x = -396\)

Now divide by 12 to solve for x.

\(\displaystyle x = -\frac{396}{12}\)

Here, because one of the numbers in the equation is positive, and the other is negative, the answer must be a negative number:

\(\displaystyle x = -33\)

To evaluate this, rewrite the expression with the correct signs.

Positive multiplied with a negative sign results in a negative, and a double negative results in a positive sign.

\(\displaystyle -2-(-6)-2+(-3) = -2+6-2-3=-1\)

It is possible to rewrite the expression as:

\(\displaystyle -(47-23)\)

Take the negative of the difference of 47 and 23.

The answer is \(\displaystyle -24\).

Evaluate the inner term inside the parenthesis first.  The expression can then be simplifed to an integer.

\(\displaystyle -2-(3+2) = -2-5 = -7\)