\(\displaystyle -6\times-8+7=(-6\times-8)+7=48+7=55\)

\(\displaystyle -3-7=-10\)

The problem indicates that the result is \(\displaystyle 7\) units more negative than \(\displaystyle -3\), which is \(\displaystyle -10\).

Substitute 8 for \(\displaystyle x\) in the expression and evaluate, paying attention to the order of operations:

\(\displaystyle -16 + x^{2}\)

\(\displaystyle =-16 + 8^{2}\)

\(\displaystyle =-16 + 64\)

\(\displaystyle = + \left (64-16 \right )\)

\(\displaystyle = 48\)

This is a straightforward problem. Remember that when adding a negative number, you are actually subtracting:

\(\displaystyle \small a+-b = a-b\)

Be sure to remember that the first number is also negative, meaning we are subtracting a number from a negative number:

\(\displaystyle \small -3.5+-2.75\)

\(\displaystyle \small =-3.5-2.75\)

\(\displaystyle \small =-6.25\)

The answer is -6.25.

The sum of two numbers of unlike sign is the difference of their absolute values, with the sign of the "dominant" number (the positive number here) affixed:

\(\displaystyle -3.2+7.17 = +(7.17 - 3.2) = 7.17 - 3.2\)

Subtract vertically by aligning the decimal points, making sure you append the 3.2 with a placeholder zero:

\(\displaystyle 7.12\)

\(\displaystyle \underline{3.20}\)

\(\displaystyle 3.97\)

This is the correct choice.

To make \(\displaystyle b-a\) as small as possible, let \(\displaystyle b\) be as small as possible \(\displaystyle (b=-1)\), and subtract the largest value of \(\displaystyle a\) possible \(\displaystyle (a=4)\):

\(\displaystyle -1-4=-5\)

To solve this problem, you need to get your variable isolated on one side of the equation:

\(\displaystyle 2x + 47 = -47\)

\(\displaystyle 2x + 47 + (- 47) = -47 + (-47)\)

Taking this step will elminate the \(\displaystyle 47\) on the side with \(\displaystyle x\):

\(\displaystyle 2x = -94\)

Now divide by \(\displaystyle 2\) to solve for \(\displaystyle x\):

\(\displaystyle x = -\frac{94}{2}\)

\(\displaystyle x = -47\)

The important step here is to be able to add the negative numbers.  When you add negative numbers, they create lower negative numbers (if you prefer to think about it another way, you can think of adding negative numbers as subtracting one of the negative numbers from the other).  

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 \(\displaystyle x=2\)

To solve this equation, you need to isolate the variable on one side. We can accomplish this by dividing by \(\displaystyle -3\) on both sides:

\(\displaystyle -3y = -45\)

\(\displaystyle y = \frac{-45}{-3}\)

Anytime you divide, if the signs are the same (i.e. two positive, or two negative), you'll get a positive result.  If the signs are opposites (i.e. one positive, one negative) then you get a negative.  

Both of the numbers here are negative, so we will have a positive result:

\(\displaystyle y = 15\) 

To solve, you need to isolate the variable. We first subtract \(\displaystyle 18\) then divide by \(\displaystyle 2\):

\(\displaystyle 2p + 18 = 12\)

\(\displaystyle 2p = -6\)

\(\displaystyle p = \frac{-6}{2}\)

When dividing, if the signs of the numbers are the same (i.e. both positive, or both negative), you yield a positive result.  If the signs of the numbers are opposites (i.e. one of each), then you yield a negative result.  

Therefore:

\(\displaystyle p = -3\)