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Honestly, I think most of these things are pretty obvious if everyone just uses common sense.

A note about how I will participate in the discussion boards:

• Remember that you are not supposed to do the work for someone else; you are trying to give them help. Tell them what to do next, find where they made a mistake in their work, or explain something they aren't getting; don't just give them the problem all worked out.
  
  
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• If you need to refer to part of the original post, I suggest you cut and paste the parts you need to make it clear where the mistake occurred.
  
  
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On pg 131, prob 37:

Simplify:
-5x (3x^2 - 2x) + 7x^2

= -15x^3 - 10x + 7x^2
= -15x^3 + 7x^2 - 10x 

But the answer manual 
says -15x^3 + 17x^2 
What did I do wrong? 

Check your signs, doofus.

You distributed through the 
parenthesis wrong.

When you multiplied through
the parenth. here:
-5x (3x^2 - 2x) + 7x^2


you forgot to multiply
the -5x times -2x, so 
you should have gotten:


= -15x^3 + 10x^2 + 7x^2


Combine like terms now...

In response to this (different) question:

Solve:
3 (x - 4) - 2 = 5x + 7
3x - 12 - 2 = 5x + 7
3x - 14 = 5x + 7


What is the next
step? I know I need to
get it to look like
x = 5 (or whatever) How?

You work it like this:
3 (x - 4) - 2 = 5x + 7
3x - 12 - 2 = 5x + 7
3x - 14 = 5x + 7
-2x = 21
x = -21/2

For the next step, you
need to get all the x's
on one side and the 
numbers on the other. If
we move all the x's to
the left side:
3x - 14 - 5x = 5x + 7 - 5x
-2x - 14 = 7


We can then move the
numbers to the right
side:
-2x - 14 + 14 = 7 + 14

-2x = 21



Now finish it.

Get all x's on one side 
and all numbers on other.
3x - 14 - 5x = 5x + 7 - 5x
-2x - 14 = 7
-2x - 14 + 14 = 7 + 14
-2x = 21

Now finish

• Use the following symbols:
  • Multiplication: * (so 2*3)
  • Division: / (so 5/7)
  • Powers: ^ (so 3^2 = 9, or x^3)
  • Absolute value: | (so |-7| = 7; you find this symbol on the \ key)
• Use plenty of parentheses. This is especially true when writing fractions. Here are some examples:
  • x - 4 / 7 isn't clear; does this mean x - (4/7) or (x-4)/7?
  • 3x / (x-2)
  • (2/3) - (-3/5)
• Add in some extra spaces around +, -, and =. It is just easier to read.

Examples: (These examples are from a Basic Math Skills course that I borrowed from Mary Parker, but the basic issues are the same. You probably won't need to show quite as many steps when you do your work. Think of it as a quick review of some Basic Math skills...)

In many cases there are easier and better ways to show the
work using paper and pencil. Use those easier and better
ways as you do homework and on the test.

Example 1: Factor 252 completely.

Solution:
252 = 2 * 126
= 2 * 2 * 63
= 2 * 2 * 7 * 9
= 2 * 2 * 7 * 3 * 3
= 2 * 2 * 3 * 3 * 7

Comments: Notice that, although the factor tree is a nice
way to find the factors, it is not convenient to put it into
an email message. And, on tests, sometimes students show
the factor tree, but neglect to show the final factored
form for the answer. So it is good to practice this.
Also, notice that it is not convenient to show exponential
notation using only text. You should be able to show
exponential notation when you take the test, of course.)

Example 2: Solve 4*5+7*10 = 4x + x

Solution:
4*5+7*10 = 4x + x
20+70 = 5x
90 = 5x
90/5 = 5x / 5
18 = x

Comments: Sometimes students prefer to skip steps.
On a test, you must show all steps to get full credit.
Even in working problems for practice, you should write
all the steps until you can see them in your mind so
clearly that you don't need to write them in order to see them.

Example 3: Multiplying fractions:
Do the indicated operation: (12/35)*(14/45)

Solution:
(12/35)*(14/45)
= (12*14) / (35*45)
= (2*6*2*7) / (5*7*9*5)
= (2*3*2*2) / (5*3*3*5)
= (2*2*2)/(5*3*5)
= 8/75

Comments: Many students actually multiply together the
two numerators and the two denominators in the first step.
They get large numbers and then have to reduce the
resulting fraction. Since the numbers are so large,
many students make mistakes in reducing. It is much
easier to indicate what should be multiplied and then
factor them before multiplying to get large numbers.
Then it is easy to see how to reduce the fraction.

Example 4: Adding fractions.
a. Find a common denominator for 28 and 42. Show all work.
b. Use that to add 11/28 + 5/42. Show the equivalent
fractions and your answer.

Solution:
a. 28=2*2*7 and 42=2*3*7, so denom = 2*2*3*7 = 84
b. 11/28 + 5/42
= 11/(2*2*7) + 5/(2*3*7)
= (11*3)/(2*2*7*3) + (5*2)/(2*2*3*7)
= 33/84 + 10/84
= (33+10)/84
= 43/84

Comments:
Students often want to find the common denominator by
"inspection." That doesn't work in all cases. It's a
good idea to use a method that will always work. And,
of course, remember that you only need to find a common
denominator when adding or subtracting fractions,
NOT when multiplying or dividing fractions.

Example 5: Solving percent problems.
To find the selling price of a TV, the dealer multiplies
the wholesale price by 130%. If the selling price of a
particular TV was $195, what is the wholesale price of the TV?

Solution: Let x = the wholesale price

Wholesale price / wholesale percent = original price / original percent
x/100 = 195/130
x*130 = 195*100
(x*130)/130 = (195*100)/130
x = 150
So the wholesale price is $150.

Comments: There are several different ways to correctly
write the ratios needed here, but there are also some
incorrect ways. To receive full credit for your solution,
you must show the ratios you use and they must be correct.
See my supplemental handout on this section for more
discussion of the ratios.

Example 6: Order of operations: Perform the indicated
operations and simplify.
16 + 20 / 5 * 2 - (-7)
= 16 + 4 * 2 - (-7)
= 16 + 8 - (-7)
= 24 + ( +7)
= 31

Comments: Sometimes students can get the correct answer
while doing more than one operation per step. But almost
no one can reliably get them correct in that fashion.
Show all steps, one at a time. Also, students often do
not notice that the rule says "multiplications and divisions,
in order, from left to right." In this problem, that means
the division comes before the multiplication, since the
division comes first.

Example 7: Adding positive and negative numbers
Simplify: -13 - (-4) - 8 + (-6)

Solution:
-13 - (-4) - 8 + (-6)
= -13 + (+4) + (-8) + (-6)
= -9 + (-8) + (-6)
= -17 + (-6)
= - 23

Comments: Students who try to do problems like these
in any fashion less well-organized than this almost
always miss some of them on tests.
1. Replace each subtraction with addition of the opposite.
2. Keep each step equivalent to the one before it.
3. Do one operation in one step.
4. Keep doing steps until you have done all the operations.

Example 8:

Find the perimeter and area of the figure in p. 457, F5.2 #136.
(This figure is a rectangle surmounted by a semicircle. The triangle
at the bottom of the figure is not relevant either to the area or
perimeter of the overall figure.)

Solution:

Perimeter = distance around the circular part of the semicircle +
length of bottom + length of left side + length of right side

perimeter = (1/2)*(2*pi*r) + 15 + 4.2 + 4.2
perimeter = 23.55 + 15 + 8.4
perimeter = 46.95 meters

area = area of semicircle + area of rectangle
area = (1/2)*(pi*r^2) + l*w
area = (1/2)*(3.14* 7.5^2) + 15*4.2
area = 88.3125 + 63
area = 149.3125 meters^2

Comments:

1. Notice that the radius of the semicircle is 15/2 = 7.5

2. Recall that the perimeter of a circle is 2*pi*r and since
this is half a circle, we need half that for the perimeter
of the semicircle. Use the same idea for the area.

3. Notice also that all measurements are in meters and so the
result for the perimeter will be in meters and the result for
the area will be in square meters.

4. Also notice that I denote the square of a number as 3*3=3^2=9

Example 9:

Convert 30 miles per hour to feet per second.

Solution: Need miles / hour = feet / second
So we need to divide by miles and multiply by feet
to get the length done. That's 5280 feet / 1 mile.

And we need to multiply by hours and divide by seconds.
We can do that in one step or two steps.
Here's how to condense two steps to one:
(hours / minutes) * (minutes / seconds)
So we have: (1 hours / 60 minutes) * (1 minutes / 60 seconds)
= 1 hour / 3600 seconds (canceling out the minutes.)

So

(30 miles) / 1 hour
= (30 miles / 1 hour ) * (5280 feet / 1 mile) * (1 hour / 3600 seconds)
= (30 * 5280 * 1) / (1 * 1 * 3600) (feet / seconds)
= ( 5280) / (120) feet/second
= 44 feet/second

Example 10: Solve 0.2x + 1.8 = 3.2

Solution:
0.2x + 1.8 = 3.2
0.2x + 1.8 - 1.8 = 3.2 - 1.8
0.2x = 1.4
0.2x / 0.2 = 1.4 / 0.2
x = 7

Example 11: The measurement of the second angle of a triangle is 30 degrees
more than the measurement of the first angle. The measurement of the third angle
is 22 degrees less than twice the measurement of the first angle. What are the
measurements of all three angles?

Solution: Let x = measurement of the first angle
Let x + 30 = measurement of the second angle
Let 2x - 22 = measurement of the third angle
first + second + third = 180
x + x + 30 + 2x - 22 = 180
4x + 8 = 180
4x + 8 - 8 = 180 - 8
4x = 172
4x / 4 = 172/4
x = 43
So the first angle is 43 degrees.
Second: x + 30 = 43 + 30 = 73 degrees
Third: 2x - 22 = 2(43) - 22 = 86 - 22 = 64 degrees

Check: Since the three angles of a triangle must sum to 180, we add these and see what it equals. 43 + 73 + 64 = 180.
So it checks!
Answer: The triangle has angles of 43 degrees, 73 degrees, and 64 degrees.