Error check my notes, please.

Hello all, was hoping that someone could check my notes for me, I would like to check for errors before I move on to other parts of the chapter.

Pre-Algebra, notes from Chapter_#03

3.1 Simplifying Algebraic Expressions

Combine Like Terms:

Algebra Rule: Do not write the coefficients of 1, or –1
X = 1, –X = -1

Adding terms:
1. If the terms have the same sign add their absolute values, and keep that same sign. 2 + 3 = 5, -2 + (-3) = -5, -2 – 3 = -5
2. If the terms have the opposite sign, subtract the smaller from the larger, and keep the sign of the larger sign. 2 + (-3) = -1, -2 + 3 = 1

Example_#01:Simplify by combining like terms

a. 3x + 2x = (3 + 2)x = 5x

b. y – 7y = (1y – 7y) = (1 - 7)y = -6y

c. 3x2 + 5x2 – 2 = (3 + 5x)2 – 2 = 8x2 - 2
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Practice Problems_#01

a. 8m – 11m = -3m, that is
(8 – 11 = -3), also (11 – 8 = 3)
b. 5a + a = 6a, that is
(5 + 1 = 6), also (1 + 5 = 6)
c. –y2 + 3y2 + 7 = 2y2 + 7, that is
(-12 + 32 + 7 = 15), but 15 is only a commutative part of the answer that we are looking for, so then in normal mathematics 15 would be correct and we would look no further, but in algebra we are more interested in the sub parts that make up our answers. In algebra the correct answer is then (2y2 + 7). Now as you look at this you might think that (22 + 7 = 11), that is to have (2 * 2 + 7 = 11), but realize that (32 + 7 = 16), that is (3 * 3 + 7 = 16). In order to get to the correct algebra answer we need to also combine the term (-y2) that is to calculate (-12) in the overall equation.

Example_#02: Simplify

2y – 6 + 4y + 8 = 6y + 2

(4y + 2y = 6y)

(8 – 6 = 2)

Answer: (6y + 2)
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Practice Problem_#02: Simplify

8m + 5 + m – 4 = 9m + 1

(8m + m = 9m)

(5 – 4 = 1)

Answer: (9m + 1)
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Example_#03: Simplify

6x + 2x – 5 = 8x - 5

(6x + 2x = 8x)

No further calculations can to be done to the (-5), so we just write it after the (8x).

Answer: (8x - 5)
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Practice Problem_#03: Simplify, combine like terms

7y + 11y – 8 = 18y – 8

(7y + 11y = 18y)

No further calculations can to be done to the (-8), so we just write it after the (18y).

Answer: (18y - 8)
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Practice Problem_#04: Simplify, combine like terms

2y – 6 + y + 7 = 3y + 1

(2y + y = 3y)

(7 – 6 = 1)

Answer: (3y + 1)
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Practice Problem_#05: Simplify, combine like terms

-9y + 2 – 4y – 8x + 12 - x = -13y – 9x + 14

(-9y + 4y = -13y)

(8x + x = 9x)

(2 + 12 = 14)

Answer: (-13y – 9x + 14)
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Example_#04: Simplify

4x + 2 – 5x + 3 = -1x + 5, or –x + 5

(4x + 5x = -1x)

(2 + 3)

Answer: (-1x + 5), or (-x + 5)
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Example_#05: Simplify

2x – 5 + 3y + 4x – 10y +11 = 6x – 7y + 6

(2x + 4x = 6x)

(10y – 3y = -7y)

(11 – 5 = 6)

Answer: (6x – 7y + 6)
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When writing the final answer write the terms in alphabetical order a, b, c, and also x, y, z

5x + x = 6x
6x + 2x = 8x
6x – 2x = 4x
-4x + 5x = x
4x – 5x = -x
-5x – 3x = -8x
-x – x = -2x
-3x – 4 + 2x + 6 = -x + 2
x – 2 – 4x – 5 = -3x – 7
4x + y – 2x + y = 2x + 2y
3x – y = 8x + 2y = 5x + y

Combining unlike terms

2a + 3b, then (2 + 3 = 5), so 2a + 3b = 5ab
2a + 3b + 4a – 5ab = 6a + 3b – 5ab

(2a – 3b + c) + (5a – 6b + c) = 7a – 9b + 2c

(2a + 5a = 7a)
(3b + 6b = 9b)
(c + c = 2c)

4xy – 9yx = -5xy
9xyz + 3yzx + 5zxy = 17xyz
(5x - 4) – (2x - 3) = 3x – 1
(5x – 2x = 3x)
(4 – 3 = 1)
Answer: (3x - 1)

Rules for removing parentheses

Parentheses either will be preceded by the add sign (+), (a + (b – c + d)), or by the subtract sign (-), (a – (b – c + d)).

When Parentheses are preceded by the add sign (+), you can simply remove them and nothing else will change: (a + (b – c + d)) = a + b – c + d.

When parentheses are preceded by the subtract sign (-), you change the sign of every term within the parentheses, (a – (b – c + d)) = a – b + c – d.

Also brackets [], and braces {} have the same function as parentheses.

Multiplying Expressions

Like signs produce a positive number, and unlike signs, produce a negative number.
-5(-2) = 10, 5(-2) = -10

Example_#06: Multiply

5(3y) = (5 * 3)y = 15y

(5 * 3 = 15)

Answer: (15y)
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Example_#07: Multiply

-2(4x) = (-2 * 4)x = -8x

(-2 * 4 = -8)

Answer: (-8x)
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Practices Problem_#06: Multiply

7(8a) = 56a

(7 * 8 = 56)

Answer: (56a)
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Practice Problem_#07 Multiply

-5(9x) = -45x

(-5 * 9 = -45)

Answer: (-45x)
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Distributive Property

(2 * 3 + 3 * 2 = 12), or (3 * 2 + 2 * 3 = 12)

2(3 + x) = 6 + 2x, that is (2 * 3 + 2 * x = 8x), but (8x) is not the answer that we are looking for, so we need to re-calculate to come to the correct answer.

(2 * 3 = 6)

(2 * x = 2x)

Answer: (6 + 2x)
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Example_#08: Multiply by using the distributive property

6(x + 4) = 6x + 24

(6 * x + 4 * 6 = 30)

(6 * x = 6x)

(6 * 4 = 24)

(6 + 24 = 30)

Answer: (6x + 24)
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Practice Problem_#08: Multiply

7(y + 2) = 7y + 14

(7 * y + 2 * 7 = 21)

(7 * y = 7y)

(7 * 2 = 14)

(7 + 14 = 21)

Answer: (7y + 14)
==

Example_#09: Multiply

-3(5a + 2) = -15a – 6

(-3 * 5 + 2 * -3 = -21)

(-3 * 5a = 15a)

(-3 * 2 = -6)

(-15 – 6 = -21)

Answer: (-15a - 6)
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Practice Problem_#09: Multiply

4(7a - 5) = 28a – 20

(4 * 7 – 5 * 4 = 8)

(4 * 7a = 28a)

(4 * 5 = 20)

(28 – 20 = 8)

Answer: (28a - 20)
==

Example_#10: Multiply

8(x - 4) = 8x – 32

(8 * x – 4 * 8 = -24)

(8 * x = 8x)

(8 * 4 - 32)

(8 – 32 = -24)

Answer: (8x - 32)
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Practice Problem_#10 Multiply

6(5 – y) = 30 – 6y

(6 * 5 – y * 6 = 24)

(6 * 5 = 30)

(6 * y = 6y)

(30 – 6 = 24)

Answer: (30 – 6y)
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Example_#11: Multiply and simplify and combine like terms

2(3 + x) – 15 = 2x + (-9), or 2x – 9

(2 * 3 + x * 2 + -15 = -7)
(6 + 2x + (-15) = -7)

(2 * x = 2x)

(2 * 3 – 15 = -9)

(2 + -9 = -7, or 2 – 9 = -7)

Answer: (2x + (-9), or 2x - 9)
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Practice Problem_#11: Simplify

5(y – 3) – 8 + y = 6y - 23

(5 * y – 3 * 5 – 8 + y = -17)

(5 * y + y = 6y)

(5 * 3 + 8 = 23)

(6 – 23 = -17)

Answer: (6y - 23)
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Example_#12: Simplify

-2(x – 5) + 4(2x + 2) = 6x + 18

(-2 * x – 5 * -2 + 4 * 2x + 2 * 4 = 24)

(-2 * x = -2x)

(4 * 2x = 8x)

(-2x + 8x = 6x)

(2 * 5 = 10)

(4 * 2 = 8)

(10 + 8 = 18)

(6 + 18 = 24)

Answer: (6x + 18)
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Example_#13: Simplify

-(x + 4) +5x + 16 = 4x + 12

(-(x + 4) + 5x + 16 = 16)

(-1 * x + 5x = 4x)

(16 – 4 = 12)

(4 + 12 = 16)

Answer: (4x + 12)
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Practice Problem_#13: Simplify

-(y + 1) + 3y - 12 = 2y – 13

(-(y + 1) + 3y – 12 = -11)

(-1 * y + 3y = 2y)

(-12 – 1 = -13)

(2 – 13 = -11)

Answer: (2y – 13)
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Example_#14: Find the perimeter of the triangle

2z + 3z + 5z = 10z, ft

Answer: (10z), ft
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Practice Problem_#14: find the perimeter of the square

2x + 2x + 2x + 2x = 8x, centimeters

Answer: (8x), centimeters
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Example_#15: find the area of the rectangle

Area = Length * Width

5 meters, 2x – 7 meters

5(2x - 7) = 10x – 35, meters

(5 * 2x – 7 * 5 = -25)

(5 * 2x = 10x)

(-7 * 5 = 35)

(10 – 35 = -25)

Answer: (10x - 35), meters
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Practice Problem_#15: find the area of the rectangle

Area = Length * Width

3 yards, 12y + 9, yards

3(12y + 9) = 36y + 27

(3 * 12y + 9 * 3 = 63)

(3 * 12y = 36y)

(3 * 9 = 27)

(36 + 27 = 63)

Answer: (36y + 27), sq yd
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Geesh...you love typing Red?

-(x + 4) +5x + 16 = 4x + 12

what's wrong with keeping it short?

remove brackets: -x - 4 + 5x + 16
similars together: -x + 5x - 4 + 16
wrap up: 4x + 12

No I don't like doing all that much typing, but it was nessary to un-boogle all those hand written notes into something that could be understood. Thanks for the infomation.

You may wish to cut it down to a problem or two, rather than a large collection.

Hi, I thought it's very diversed in the different way that algebra is done, but thanks for you thoughts.

redranger7018 said:

Practice Problem_#08: Multiply

7(y + 2) = 7y + 14

(7 * y + 2 * 7 = 21) This is not true!! I sure wouldn't include incorrect things in your notes!

(7 * y = 7y)

(7 * 2 = 14)

(7 + 14 = 21)Why is this here? the 7y and 14 are not like terms....you can't add them!

Answer: (7y + 14)
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Example_#09: Multiply

-3(5a + 2) = -15a – 6

(-3 * 5 + 2 * -3 = -21)While -15 + (-6) is indeed -21, that's NOT what you have in your problem. One of your terms involves the variable "a", and the other doesn't. So, you would NOT be combining these coefficients.

(-3 * 5a = 15a)

(-3 * 2 = -6)

(-15 – 6 = -21)See above comment. Including this in your notes may lead to confusion later on.

Answer: (-15a - 6)
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Area = Length * Width

5 meters, 2x – 7 meters

5(2x - 7) = 10x – 35, meters You're multiplying meters by meters. You should have meters^2, or square meters, as the unit for your answer.

(5 * 2x – 7 * 5 = -25) NOT TRUE. You can't combine a term containing "x" with one that doesn't.

(5 * 2x = 10x)

(-7 * 5 = 35)

(10 – 35 = -25) This does not provide any useful information for your problem. Don't include it in your notes.

Answer: (10x - 35), meters As previously noted, the unit should be meters^2 or sq. meters.
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Practice Problem_#15: find the area of the rectangle

==

Click to expand...

I am certainly an advocate of taking good notes. And I applaud your effort. However, you can show the correct process without writing so much (and certainly without including inaccurate and potentially misleading information).

Here's how I would show that first problem:
7(y + 2)
7*y + 7*2
7y + 14

DONE.....no need to write anything else.

I did not read through all of your notes.....so there may be some other errors.

Mrspi said:

I did not read through all of your notes.....so there may be some other errors.

Click to expand...

This is my point. There is just so much to read. We have only volunteers, here. We cruise by when we have the time. Just looking at all that text says to me that I don't have the time to look at it. Keep it brief. Review the response with the rest of your work. See if we don't manage to provide something that will be helpful more generally that just for the one you posted.

redranger7018 said:

Example_#02: Simplify
2y – 6 + 4y + 8 = 6y + 2
(4y + 2y = 6y)
(8 – 6 = 2)
Answer: (6y + 2)
==
Practice Problem_#02: Simplify
8m + 5 + m – 4 = 9m + 1
(8m + m = 9m)
(5 – 4 = 1)
Answer: (9m + 1)

Click to expand...

Also, there is no need to post both of these: one is sufficient, since both are done
exactly the same way. There are other similar examples of unnecessary posts.

And don't you go threatening us with "student abuse"; we're only trying to help :shock:

Hi everyone, I'd like to thank all those that have taken the time to help me clarify my notes. My notes are actually written in ms-word and are color coded. The reason is I’m dyslexic. Although I don’t see words, letters, or numbers reversed I do re-organize them in the wrong order, which makes algebra extremely difficult for me.

As far as the way I’m doing things my instructor has approved of this method

Practice Problem_#08: Multiply

7(y + 2) = 7y + 14

(7 * y + 2 * 7 = 21) realized not the correct answer, as part of that answer

(7 * y = 7y)

(7 * 2 = 14)

(7 + 14 = 21) realized not the correct answer, as part of that answer

Answer: (7y + 14) this is the only correct answer I have

So you all see I'm not a one bit stupid, just confused.

I check my hand written notes against my ms-word version and there are a few type "o's". again, thanks four your help.

redranger7018@iowatelecom.net