NinjaDevo

I'll do the first two for you to show you how to do it, then have you try the other ones.

19) 2 + 6 + (−7) + 10

Start from the left and work our way right, becuase these are all addition and subtraction. If we multiplication, division, exponets or something like that we would do those first.

2 + 6 + (−7) + 10

8 + (-7) + 10

Now we have 8 + (-7). We don't really need this positive sign, so we get 8 - 7. The rule here is that adding a negative is the same thing as subtracting a poisitve.

8 + (-7) + 10

8 -7 + 10

1 + 10

11

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20) (−5) + (−8) + (−2) + 1

Again, just addition and subtraction so we work our way from the left to the right.

(−5) + (−8) + (−2) + 1

Again, we are adding a negative. Like I said in the last problem, this is really like subtracting a positive.

(−5) + (−8) + (−2) + 1

(−5) −8 + (−2) + 1

Right now we "owe" -5. Then we loose another 8. We end up with -13.

(-13) + (−2) + 1

(-13) −2 + 1

(-15) + 1

Now we "owe" -15, and we get one. We now don't owe as much, we only owe -14.

(-14)

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Let me know if you need help with the others, but don't just say "I can't do the other ones." Tell me what you don't understand and I can then help you out.

I just answered a question like this yesterday.

Sure thing, I'll add that.

He has 50 marbels made up of the colors green, blue, and red. Let's have r = red marbles, b = blue marbles, and g = green marbels.

This means:

r + b + g = 50

He has 6 more red marbels than blue marbels. This mean r = b+6, right? Let's put this in for r.

r + b + g = 50

(b+6) + b + g = 50

He has 4 fewer green marbles than blue marbels, so g = b-4. Let's put that in.

(b+6) + b + g = 50

(b+6) + b + (b-4) = 50

And now we just solve for b, which tells us the number of blue marbels.

(b+6) + b + (b-4) = 50

b + 6 + b  + b - 4 = 50

b + b + b + 2 = 50

3b + 2 = 50

     - 2    - 2

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3b = 48

÷3    ÷3

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b = 16

So there are 16 blue marbels.

Consider the example (-3)²

This is really saying (-3) x (-3) = (-(-9)) = (9)

This only works for even exponets though. I'll show you with the example (-2)³

This is really saying (-2) x (-2) x (-2) = (-(-4)) x (-2) = (-(-(-8))) = (-8)

If you don't have parentheses, your basically imagining that there are parentheses after the negative sign. So, say you had -4²

In your head your thinking -(4²) = -(4 x 4) = -(16) = -16

Does this help you out at all?

First we have to make sure that the denominators (bottom numbers of the fractions) are the same. They are so we can now continue.

Subtracting a negative is really the same thing as adding a positive. Negatives will switch the direction you go on a number line, so subtracting a negative will make you go to the right on a number line, thus making you add that number.

$$$\frac{-330}{72} - (\frac{-216}{72})$\\\\
This is really:\\\\
$\frac{-330}{72} + (\frac{+216}{72})$\\\\
Now we can add the top numbers \\\\
$\frac{-330 + 216}{72}\\\\
\frac{-114}{72}\\\\
-1\frac{42}{72}$\\\\
Reduce by dividing the top and bottom of the fracion by 6\\\\
$-1\frac{7}{12}$\\\\
And that's it!$$

$$We have to start with subtracting 5 from both sides. We don't multiply both sides by 2 first, because that is associated with y. Think of it being tied to y, and we have to get rid of everything else before we can untie that.\\
So, we have:\\\\
$\frac{y}{2}+5=-12$\qquad \qquad Subract 5 from both sides\\\\
$\frac{y}{2}=-12-5$\\\\
$\frac{y}{2}=-17$\qquad \qquad Multiply both sides by 2\\\\
$y = -17 \times 2\\\\
y = -34$$

To divide two two fractions, multiply by the recriprocal of the second fraction.

Some people like to remember this by SKIP, CHANGE, FLIP.

And now just multiply the top and botoms together.

$$\begin{array}{l}
\frac{3}{4} \times \frac{8}{5}\\\\
\frac{3\times8}{4\times5}\\\\
\frac{24}{20}\\\\
1\frac{4}{20}\\\\
1\frac{1}{5}
\end{array}$$

I have a question for you CPhill.

To find the slope you did

$$slope= \frac{y_1 - y_2}{x_1 - x_2}$$

I thought it was

$$slope = \frac{y_2 - y_1}{x_2 - x_1}$$

Will both of these always give the same answer?

I don't doubt your answer, I was just curious.

I'm thinking you want to simplify 4a^4-4

If so, start by subtracting the exponets.

4a^4-4

4a¹

which is really just

4a

And that's it. Let me know if this isn't what you meant.