You can put this solution on YOUR website!






For more problems like this, together with an explanation that may be easier to understand than the one in your expensive textbook, please see my own website!

To find my website click on my tutor name "rapaljer" anywhere in algebra.com. There you will find a link to take you to my website. On the Homepage of my website, look for the link near the top of the page "Basic, Intermediate, and College Algebra: One Step at a Time." Next, click on "Basic Algebra", then look in Chapter 5, amd click on Section 5.03 Adding and Subtracting Square Roots. Near the top of this page there is a link to my "Math in Living Color" pages where many of these problems are solved in detail IN COLOR!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

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4!= 4*3*2*1=24

Please see my brand new page on Introduction to Statistics on my website!! I wrote it a long time ago, but it's still relevent. To find my website click on my tutor name "rapaljer" anywhere in algebra.com. There you will find a link to take you to my website. On the Homepage of my website, look for the link about a third of the way down the page "Introduction to Statistics."

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
The trick with the square root of x^2 is that this is a variable, and the answer must be a positive number.

This is why the .



Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
I have a complete explanation on this topic on my website. To find my website click on my tutor name "rapaljer" anywhere in algebra.com. There you will find a link to take you to my website. On the Homepage of my website, look for the link near the top of the page "Basic, Intermediate, and College Algebra: One Step at a Time." Next, click on "Intermediate Algebra", then look in Chapter 5, amd click on Section 5.03 Finding the Equation of a Line. Look for problems #33 and 34. Then near the top of this page there is a link to my "Math in Living Color" pages where these problems are solved in detail IN COLOR!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
P=a+b+c

36=12+8 + c
36=20+c
36-20=20-20+c
16=c
c= 16 cm.

Check: See if the 3 sides add up to 36.
12+8+16=36 It checks.

Dr. R^2

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This is an EASY one. Just let x= 8, plug it into the given equation, and see if y comes out to 1!!

y=19x+13
y=19*8+13

You don't even need to calculate this to see that it is NOT 1!! So this point is NOT a solution of the given equation.

Dr. R^2

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This one is MUCH easier than it looks!! You have to ask yourself, "What makes a fraction UNDEFINED?" The answer is "DENOMINATOR = ZERO."

So, make the denominator equal to zero (which we ALL know is NEVER really allowed in math!!), and solve the equation.




x= 2 or x= -2

Dr. R^2

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Since you are starting out with the fraction 7/15, and you want to end up with a denominator of 105c, you have to compare the denominators of the two fractions to see what is "Missing" from the first denominator. In other words, what would you multiply 15 by in order to get 105c? The trick is to divide 15 into 105c, and see what you get! It turns out to be 7c.

So, multiply the fraction by 1, which in this case is , and you get
, which is .

If you like my explanation here, then you really need to see my own explanation of FRACTIONS on my own website! To find my website, just click on my tutor name "Rapaljer" anywhere in algebra.com. There you will find a link that takes you right to my Homepage. From my homepage, look for the link "Basic, Intermediate, and College Algebra", then select "Basic Algebra". The FRACTIONS are in Chapter 3, so look for Sections 3.03 and 3.04. Here I hope you will like my own "user-friendly" explanations, examples, exercises, ALL with answers too. My own students used to tell me that these are a LOT easier to understand than the traditional textbooks that were written by mathematicians for other mathematicians and publishers! What I have to offer is completely FREE!

Many of the problems in my sections are solved in detail in the corresponding "MATH IN LIVING COLOR" pages. (In fact, the fast way to find my website is to do a Google search for "Math in Living Color", and then take the link at the bottom of this page to go back to my Homepage.)

Anyway, I have a LOT of pages that may be helpful to you including my complete curriculum and a lot of solutions in COLOR to help you understand. There are also VIDEOS (on a variety of topics!) of me teaching in my classes before I retired. Best of all, it's all FREE!

Dr. R^2

Dr. Robert J. Rapalje
Seminole State College of Florida

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Let x = the first number
3x = second number
x-6= third number

The equation is based upon the SUM of the numbers:
x+ 3x + x-6 = 44
5x - 6 = 44
5x= 50
x=10

x=10 First Number
3x= 3*10=30 Second Number
x-6=4 Third Number

Check: The sum of the numbers is 10 + 30 + 4 = 44 It checks!!

Now, you really need to see my own explanation of WORD PROBLEMS on my own website! To find my website, just click on my tutor name "Rapaljer" anywhere in algebra.com. There you will find a link that takes you right to my Homepage. From my homepage, look for the link "Basic, Intermediate, and College Algebra", then select "Basic Algebra". The word problems are in Chapter 1, so look for Sections 1.09 and 1.10. Most word problems are NOT nearly as hard as they look, if you know how to set them up. This is what I tried to show you with my own "user-friendly" explanations, examples, exercises, ALL with answers too. My own students used to tell me that these are a LOT easier to understand than the traditional textbooks that were written by mathematicians for other mathematicians and publishers! What I have to offer is completely FREE!

Many of the problems in my sections are solved in detail in the corresponding "MATH IN LIVING COLOR" pages. (In fact, the fast way to find my website is to do a Google search for "Math in Living Color", and then take the link at the bottom of this page to go back to my Homepage.)

Anyway, I have a LOT of pages that may be helpful to you including my complete curriculum and a lot of solutions in COLOR to help you understand. There are also VIDEOS (on a variety of topics!) of me teaching in my classes before I retired. Best of all, it's all FREE!

By the way, if you REALLY need this to be solved by Systems of Equations Methods, please send me an Email, and I'll be glad to solve it for you that way.

Dr. R^2

Dr. Robert J. Rapalje
Seminole State College of Florida

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The slope of a line is the RISE OVER the RUN. It's the DIFFERENCE in the y coordinates divided by the DIFFERENCE in the x coordinates.
In this case slope =
Slope =

Check out my own explanation of SLOPE on my own website! To find my website, just click on my tutor name "Rapaljer" anywhere in algebra.com. There you will find a link that takes you right to my Homepage. From my homepage, look for the link "Basic, Intermediate, and College Algebra", then select "Basic Algebra". The Graphing and Slope explanations are in Chapter 4, so look for Section 4.05 which is called "More Slope". If you need help also with Graphing and Slope of a Line, this explanation is at the beginning of Chapter 4. Here you will find my own "user-friendly" explanations, examples, exercises, ALL with answers too. My own students used to tell me that these are a LOT easier to understand than the traditional textbooks that were written by mathematicians for other mathematicians and publishers! What I have to offer is completely FREE!

Many of the problems in my sections are solved in detail in the corresponding "MATH IN LIVING COLOR" pages. (In fact, the fast way to find my website is to do a Google search for "Math in Living Color", and then take the link at the bottom of this page to go back to my Homepage.)

There is also a VIDEO on the topic of Graphing and Slope of a Line (and also on a variety of other topics!) of me teaching in my classes before I retired. Best of all, it's all FREE!

Dr. R^2

Dr. Robert J. Rapalje
Seminole State College of Florida

You can put this solution on YOUR website!
Let x = the number
2x+7=3(x+6)
2x+7=3x+18

2x-2x+7=3x-2x+18
7=x+18
7-18=x+18-18
-11=x

Check:

Twice the number is -22, and 7 more than this is -15.

On the other side, the sum of 6 + -11 is -5. Three times this is -15, so it checks!!

Now, you really need to see my own explanation of WORD PROBLEMS on my own website! To find my website, just click on my tutor name "Rapaljer" anywhere in algebra.com. There you will find a link that takes you right to my Homepage. From my homepage, look for the link "Basic, Intermediate, and College Algebra", then select "Basic Algebra". The word problems are in Chapter 1, so look for Sections 1.09 and 1.10. Most word problems are NOT nearly as hard as they look, if you know how to set them up. This is what I tried to show you with my own "user-friendly" explanations, examples, exercises, ALL with answers too. My own students used to tell me that these are a LOT easier to understand than the traditional textbooks that were written by mathematicians for other mathematicians and publishers! What I have to offer is completely FREE!

Many of the problems in my sections are solved in detail in the corresponding "MATH IN LIVING COLOR" pages. (In fact, the fast way to find my website is to do a Google search for "Math in Living Color", and then take the link at the bottom of this page to go back to my Homepage.)

Anyway, I have a LOT of pages that may be helpful to you including my complete curriculum and a lot of solutions in COLOR to help you understand. There are also VIDEOS (on a variety of topics!) of me teaching in my classes before I retired.

Dr. R^2

Dr. Robert J. Rapalje
Seminole State College of Florida

You can put this solution on YOUR website!
Always start a word problem by identifying all the variables. By this, I mean to say "Let x = _____". In this case, there is only one variable, the unknown number, x.

Let x = the number

Then, just translate the sentence into an equation like this:
(remember that "is equal to" always means "="!)
2(x+2)=x-2
2x+4=3(x-2)

Remove the parentheses by distributive property:
2x+4=3x-6

Now, solve the equation by subtracting 2x from each side:
2x-2x+4=3x-6-2x
4=x-6

Add +6 to each side:
4+6=x-6+6
10=x
Finally, check to see if it satisfies the sentence:
The sum of the number and 2 would be 12. Twice this amount is 24. On the other side, the difference of 10 and 2 would be 8, and three times this would also be 24.

By the way, checking is always a good idea, because when I checked my original work in this problem, I MISSED IT!! I caught my error by checking it!!

Now, you really need to see my own explanation of WORD PROBLEMS on my own website! To find my website, just click on my tutor name "Rapaljer" anywhere in algebra.com. There you will find a link that takes you right to my Homepage. From my homepage, look for the link "Basic, Intermediate, and College Algebra", then select "Basic Algebra". The word problems are in Chapter 1, so look for Sections 1.09 and 1.10. Most word problems are NOT nearly as hard as they look, if you know how to set them up. This is what I tried to show you with my own "user-friendly" explanations, examples, exercises, ALL with answers too. My own students used to tell me that these are a LOT easier to understand than the traditional textbooks that were written by mathematicians for other mathematicians and publishers! What I have to offer is completely FREE!

Many of the problems in my sections are solved in detail in the corresponding "MATH IN LIVING COLOR" pages. (In fact, the fast way to find my website is to do a Google search for "Math in Living Color", and then take the link at the bottom of this page to go back to my Homepage.)

Anyway, I have a LOT of pages that may be helpful to you including my complete curriculum and a lot of solutions in COLOR to help you understand. There are also VIDEOS (on a variety of topics!) of me teaching in my classes before I retired. Best of all, it's all FREE!

Dr. R^2

Dr. Robert J. Rapalje
Seminole State College of Florida

You can put this solution on YOUR website!
Thank you for asking this question!! I have a LOT of explanation on the topic of FACTORING. More about that later.

In this problem, you need to see if there is a COMMON FACTOR--that is, a number or variable that divides evenly into each of the two terms in this problem. Get the largest common factor, which would be 8. So, factor out the 8, which leaves a 5p in the first term and 4r in the second term.

8(5p - 4r).

For additional help with FACTORING, please see my own website. To find my website, you can click on my tutor name "Rapaljer" anywhere in algebra.com. There you will find a link that takes you to my Homepage. On the Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose, "Basic Algebra", and look in "Chapter 2" for "Section 2.03 Factoring the Common Factor." Here you will find my own non-traditional explanation that was written especially for students who have trouble with math. My own students all told me that it was much easier to understand than the traditional textbooks. Now, my entire curriculum from Basic Algebra to College Algebra is all posted on the website FREE!!

There is also a video from my own classes before I retired of me teaching the lesson on FACTORING. You can see this video FREE from my website. On my Homepage, look for the link "Rapalje Videos in Living Color." Choose "Basic Algebra" and look for the video called "Factoring."

If you get tired of Factoring, or if you just plain hate math, then see my "Joke Page", with lots of good clean jokes, all safe for the little ears in your family!!

If you need help with this topic or with other topics, please send me an Email. I'll be glad to help you find the right page on my website to give you the help you need!!

Dr. R^2, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
Did you mean that 1 sq. m. = 1.2 sq yd? I believe this is correct. Then
30 (m^2) = 30*(1.2 sq yd)
30 m^2 = 36 sq yd (approximately!)

Dr. R^2

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I don't understand your question. Perhaps you are having trouble writing the radical expression. Is this a cube root of a fraction? In the meantime, I do have a pretty good explanation of radicals on my own website. You might want to check it out, since it is easier for most people to understand.

To find my website, you can click on my tutor name "Rapaljer" anywhere in algebra.com. There you will find a link that takes you to my Homepage. On the Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose, "Basic Algebra", and look in "Chapter 5," where the whole chapter is devoted to square roots.

If you need a more advanced explanation, you can look in "Intermediate Algebra" in Chapter 3, or in "College Algebra" in Chapter 1 for topics on Radicals.

Here you will find my own non-traditional explanation that was written especially for students who have trouble with math. My own students all told me that it was much easier to understand than the traditional textbooks. Now, my entire curriculum from Basic Algebra to College Algebra is all posted on the website FREE!! Also, most of the hardest problems in my curriculum are already solved on the MATH IN LIVING COLOR pages that go with these sections.

In addition to the written explanations, I also have several videos that were made in my own classroom before I retired. The video on Radicals was made in Basic Algebra. To see my videos FREE, look for the page on my Homepage "Rapalje Videos in Living Color." Then choose "Basic Algebra" and look for the video on "Square Roots." It's all FREE!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
y=x+2
y=-x-6

x+2=-x-6

Add +x to each side:
2x+2=-6
2x=-8
x=-4

Substitute back into the first equation:
y=x+2
y=-4+2
y=-2

Check in the second equation:
y=-x-6
-2=-(-4)-6
-2=4-6
It checks!!

For additional help with this topic, please see my own website. To find my website, you can click on my tutor name "Rapaljer" anywhere in algebra.com. There you will find a link that takes you to my Homepage. On the Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose, "Basic Algebra", and look in "Chapter 4" for Section 4.07 "Systems of Equations." Here you will find my own non-traditional explanation that was written especially for students who have trouble with math. My own students all told me that it was much easier to understand than the traditional textbooks. Now, my entire curriculum from Basic Algebra to College Algebra is all posted on the website FREE!!

Dr. R^2, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
V=s^3
V=2.5^3 = 15.625 cubic cm.

Dr. Rapalje
Seminole State College of Florida

P.S. See my website by clicking on my tutor name "rapaljer". The link there will take you to my homepage. About halfway down my homepage, look for "Topics from Geometry," and look for the link "Perimeters, Areas, and Volumes."

You can put this solution on YOUR website!
Since this is a 3 dimensional solid, when you take HALF of each dimension, you multiply the original volume by HALF for each of the 3 dimensions. The fast way to do this is to take .

V= = 6.33... cubic inches.

Dr. Rapalje
Seminole State College of Florida

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V = LWH

V1=10*10*3 = 300 cubic inches
V2= 9*9*3= 243 cubic inches

The difference = 300-243 = 57 cubic inches.

Dr. Rapalje
Seminole State College of Florida

P.S. See my website by clicking on my tutor name "rapaljer". The link there will take you to my homepage. About halfway down my homepage, look for "Topics from Geometry," and look for the link "Perimeters, Areas, and Volumes."

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Who keeps doing this???

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Looks right to me. Except that I would label the answer in the last two steps as "m perpendicular", not "y".

Dr. Rapalje

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It could actually be either way. If the jobs are two DISTINCT and SEPARATE jobs, then it is a permutation. The order matters!!

If these are two jobs, like two vacancies in an office pool, doing essentially the same task, then this is a combination. The order does NOT matter!!

P(6,2) = 6*5 = 30
C(6,2) = = 15

The problem is not completely clear to me. You decide!!

Dr. Rapalje

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To find f+g, just add them together, and combine like terms.

f+g=4x-2

If you need more help with functional notation, please see my own website. I have an entire curriculum posted on my website, all FREE. Look for the link near the top of my Homepage that says "Basic, Intermediate, and College Algebra: One Step at a Time," click on "College Algebra", and look in Chapter 2 for the topic called "The Algebra of Functions". There you will find lots of user-friendly explanation, examples, and exercises on I also have lots of problems that are solved in COLOR for you, and even videos on certain topics that may be of interest to you, videos from my own classrooms a few years ago before I retired. It's all FREE!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
Please see my own website. I have a page dedicated to the GED test. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Then click on the link that will take you to my website. From the Homepage of my website (about halfway down the page!), look for the link that says "Need help with the GED?" This has quite a few references and practice tests that will help you.

Also, if you or anyone else needs help with algebra, I have an entire curriculum posted on my website, all FREE. Look for the link near the top of my Homepage that says "Basic, Intermediate, and College Algebra: One Step at a Time," click on "Basic Algebra". There you will find lots of user-friendly explanation, examples, and exercises on nearly every topic you will need. I also have lots of problems that are solved in COLOR for you, and even videos on certain topics from my own classrooms a few years ago before I retired. It's all FREE!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
I hate when they do this!!!

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Begin by adding +39 to each side:

4+39 = -x - 39 +39
43= -x

So, -x=43

Multiply both sides by -1
x=-43

For additional explanation on Equation Solving, please see my own website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Basic Algebra", and look in "Chapter 1" for "Section 1.08". Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE!

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
You need to substitute the value of x=-4 in place of all the x's as in the following solution.

f(x) = 5x^2 -7x + 9
f(-4)=5(-4)^2-7(-4) + 9
= 5*16+28+9
= 80 +28 + 9
=117

For additional explanation on Functional Notation with a very simple explanation, please see my own website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Basic Algebra", and look in "Chapter 4" for "Section 4.09". Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE!

If you want a more advanced explanation, please see my Intermediate Algebra (Chapter 5) and my College Algebra (Chapter 2) sections on the topic of Functions, Domain, and Range. This is a topic that LOOKS hard, but it's really just like that old Glade commercial: "PLug it in, Plug it in!!!"

Check also for my VIDEO on "Functions, Domain, and Range" (if you want to go that far!) These videos were made a few years before I retired of me actually teaching this topic. To see the videos, from my Homepage, look for "Rapalje Videos in Living Color." Then click on "Intermediate or College Algebra" and look for the topic on "Functions, Domain, and Range." If you have RealPlayer installed on your computer, then this is a FREE download. If you do not have RealPlayer, then you will have to download RealPlayer, but this too is a FREE download.


I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
Let m= Number of laps for Mark
3m+5 = Number of laps for Pablo
4m= Number of laps for Faustina

The TOTAL number of laps (that means add them up!) = 29

m+3m+5 + 4m=29
8m+5 = 29
8m+5-5 = 29-5
8m= 24
m=3 Mark
3m+5 = 3*3 + 5 = 14 Pablo
4m= 4*3= 12 = Faustina

Check: 3+14+12 = 29
It checks!!

For additional explanation on WORD PROBLEMS, please see my own website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Basic Algebra", and look in "Chapter 1" for Sections 1.09 and 1.10 on Word Problems. Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE!

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
Try my own website!! To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Basic Algebra", and look in "Chapter 4" for Section 4.07 Systems of Equations." This is a complete explanation of Systems of Equations, and you will have to scroll down several pages to get the sub-section within this called "Substitution Method." Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE!

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
By definition of logarithms, means that

The trick here is to "undo" raising to the 3/2 power. This can be done by raising both sides of the equation tok the 2/3 as follows. Remember that when you raise a power to a power, you multiply the exponents. Multiply (3/2)*(2/3)=1.





For additional explanation on LOGARITHMS, please see my own website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "College Algebra", and look in "Chapter 4" for an entire chapter of LOGARITHMS. Of course, for this problem, you need to see the one called "4.01 Definition of Logarithms." Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE!

Check also for my 2 TWO-hour VIDEOS on LOGARITHMS that were made a few years before I retired of me actually teaching this topic. To see the videos, from my Homepage, look for "Rapalje Videos in Living Color." Then click on "College Algebra" and look for the logarithms topics. If you have RealPlayer installed on your computer, then this is a FREE download. If you do not have RealPlayer, then you will have to download RealPlayer, but this too is a FREE download.

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
How does that Glade commercial go: "Plug it in, plug it in!"

x=3 and y=9
3(x+7y)
3(3+7*9)

Now you have to know the order of operations to know what to calculate first. The first step is to do what is inside the parentheses, and multiplication comes befoe addition:
3(3+63)

Next, add within the parentheses:
3(66)
198

For additional explanation on topics like this, please see my own website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Basic Algebra", and look in "Chapter 1" for several topics on Signed Numbers, Order of Operations, and Variables. Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE!

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida