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Avariableis a symbol for a number we don't know yet. it is usually
y a letter like x or y.
A number on it's own is called constant.
Acoefficient is a number used to multiply a variable.
An operator is symbol that represents an operation.
Step 1 : Subtract both sides by 4 .
Step 2 : Simplify. 4-4 = 0 on the left and 14 - 4 = 10 on the right. then we need to think about how to remove the coefficient 2.
Step 3: Since the opposite of multiplication is division. I'm going to divide both sides by 2. simplify . 2/2 = 1 on the left. 10/2 = 5 on the right so the answer is x = 5.
How to model Distributive Property Step 1: Lay out the equation- 2 groups of x and 2 groups of -1 and it equals 6 Step 2: You have to create a zero pair by adding +2 and balancing out by adding +2 with 6 Step 3: You need to equally apply the 8 along with x so in this case each x equals 4 Step 4: Model out what x is (4) So x equals 4 Constant- The integer that we cancel first. It is a fixed value. Variable- A letter that represents an unknown number Coefficient- The number that is being multiplied, divided, added, or subtracted by
Steps on how to solve a 2-step equation (multiplying)
1.) Look at your equation and check which ones are the constant, variable, and co-efficient. In this equation, 3 is the co-efficient, x is the variable, and 2 and 8 are the constants.
2.) In order to isolate the variable, you get rid of the constants first by using a zero pair. If you're looking at it, + 2 will look like an integer (+2) and to make a zero pair you use the opposite operation. So, the opposite operation of (+2) is (-2). Once you have written that, whatever you do to one side, you have to do it on the other side. Also put a (-2) on the side of the equal sign.
Here, it just shows you since you have made a zero pair with the (+2 -2) You use the difference of 8-2 in the next step.
3.) Since you have made the constant disappear, you put the remaining numbers together, which will look like an easier equation. Wait, you haven't isolated the variable (x) yet because the co-efficient is still there!
4.) To get rid of the co-efficient, you must do the same steps you did to get rid of the constant. On this one though, you use the opposite operation of multiplying. How do I know 3x is supposed to be multiplied? Well, since there's no order of operations between the variable and co-efficient, it automatically multiplies! Moving on, the opposite operation of multiplying is dividing so you divide 3 with 3 to make 1. Whatever you do to one side you have to do to the other so 6 divided by 3 equals 2.
AND THEREFORE X = 2! BUT WAIT!ALWAYS VERIFY BECAUSE IT MIGHT BE THE WRONG ANSWER! If you knew the answer was x=2 still please verify because it is good practice and you never know, you might be wrong!
DON'T FORGET TO VERIFY!
Re-write the original equation again
Now you change x as 2 because that was your/my(?) answer
You use the system BEDMAS/ PEDMAS so 3(2) equals 6 (Remember the rule I said about numbers not having an operation in between them)
Definitions
Variable- A letter or a symbol that represent s an unknown number. In order to solve this problem, you will have to find what the number x's value is.
Constant- A fixed value.
Co-efficient-A number used to multiply or divide a variable
Distributive Property
I made 3 groups of x (variable) and the -2 (constant). Then, I added the the 3 groups of -2 and got -6. Which would be your next equation.
This will have similar steps from both multiplying and dividing so this step might be easy for you. In order to make a zero pair, you will have to use the opposite operation of the constant and add/subtract them. The opposite of -6 is +6, and whatever you do to one side, you do to the other. So, you also put in +6 on the side of the equal sign. making it 9+6. I then re-wrote the remaining numbers which were 3x and 15. You do the same step with this equation, so you do the opposite equation to isolate the variable x. After I did that, I got x = 5!
DON'T FORGET TO VERIFY, ALWAYS VERIFY!!
So, I re-wrote the equation again, then replaced x with what I got which is 5 and then continued on. I got it right!
How to solve a 2-step equation (dividing)
1.) Look at the equation and look for the variable you need to isolate and the co-efficient and constants you need to get rid off.
2.) -1 is the one you need to get rid off, so in order to get rid of it you use the opposite operation of -1 (which is +1). Also put a +1 on the side of the equal sign because whatever you do to one side, you have to do to the other.
3.) Once you have finished doing the last step, you re-write the remaining numbers and symbols. It's suppose to look like the second equation on the diagram. Then, you get rid of the co-efficient by doing the same step you did to get rid of -1. You use the opposite operation of division, and that is multiplying. Don't forget to do the same thing on the side of the equal sign (even though it doesn't show there haha.) So 4(3) is 12 and you write h = 12.
Then you VERIFY! ☺
Modeling
RED- POSITIVE WHITE- NEGATIVE 1.) Look at the diagram. It's a distributive property so you have to share. First you draw the diagram.
2.)Get rid of the constant by making a zero pair. Then, whichever number you added on the -1 side, you add it on to the equal sign side
3.)Then, you share them equally in two groups (because there are only 2 groups there)
4.)Since you put in two groups, you have to show how many x's are there in 1 group. So you draw it again but this time you show only 1 group! X = 4!!
Also, don't forget to verify using numbers! (Just to be sure)
*Thank you for taking the time to read my post about the different equations on Algebra. I was planning to sing because I wanted to try something out of my comfort level but I guess I wasn't ready enough and it would highly be embarrassing for me to sing by myself (especially with my really weird voice). Anyways, I hope you have learnt something from my post and good luck!☺☺ -Kathleen*
I wrote a little algebra song, its basically just about the steps you use to solve an equation. Here are the lyrics if you don't understand what I'm singing hopefully this makes much more sense.
Algebra Song
This is a song on how to multiply, two step equation and even on how to divide I'm also gonna show you distributive property, and vocabulary there's such a wide variety Like coefficient, variable and constant too I'll even show you one day that your dreams will come true Haha, I'm just kidding about the whole dreams part
To multiply you isolate the variable, it's sorta like this thing we call a symbol It's a letter that represents an unknown number Don't worry now this wont get any tougher Then you cancel the constant, a number that doesn't change You balance both sides, this order wont rearrange
Simplify, then cancel the coefficient, have I told you what that is? I don't think I have yet
It's the number that's being multiplied, then you balance both sides and you simplify
There very last step is to verify If I can say one thing, this is easy as pie
This is a song on how to multiply, two step equations and even how to divide
I'm also gonna show you distributive property, and vocabulary there's such a wide variety
Like coefficient, variable and constant too
I'll even show you one day that your dreams will come true
I'm still kidding
To divide you isolate the variable, 0 pair the constant, this should be real simple
You balance both sides and you don't simplify,
Cancel the coefficient, in this case you multiply
Balance both sides once again, then you simplify now
I hope this is all making sense
The very last step is to verify, just like I said this is easy as pie
This is a song on how to multiply, two step equations and even on how to divide
I'm also gonna show you distributive property, and vocabulary there's such a wide variety
Like coefficient, variable and constant too
I'll even show you one day that your dreams will come true
Seriously, I'm not gonna do that
The last thing left is distributive property There's a simple technique and it's very easy
You multiply the constant with the coefficient
Now the constant's changed and its something different
You still have to multiply using the variable, like I said it is a symbol
Follow all the steps for multiplication
When you do that there'll be no complication
This was my song on how to multiply, two step equations and even on how to divide
I showed you distributive property, and vocabulary with such a wide variety
Multiplying
The first thing you have to do is isolate the variable so you get rid of the +2 by adding -2. Also do that to the right side, 11-2. That's canceling the constant, the number that doesn't change. Which is why there is an X over it. Now the equation is balanced, well it always has been. When you finish that you're left with 3x=9.
Next you simplify by getting the variable by itself. You cancel the coefficient, the number that is being multiplied. You do that by dividing the number by itself, 3 divided by 3. Don't forget to do the same thing to your right side, 9 divided by 3. You now have x=3.
You balance by now using the value of x in the equation. Which is 3. You simplify by doing the first operation, which is multiplication so 3x3=9. Now you use that for the equation. So now you have 9+2=11. The last thing left is to verify, you do it to prove that the answer is right and both sides are equal, 11=11.
Dividing
The first thing you do is isolate the variable so you get rid of the +3 by adding -3. Also do it to the right side. You then balance by multiplying x over 2 by 2 because 2 is the number being divided by. Don't forget to do it to the other side as well, 4x2=8. You cancel the coefficient, using multiplying like I said and then you are left with x=8.
You balance by using the value of x in the equation which is 8. Then you simplify by doing the first operation which is dividing 8 by 2. Now you use that answer for the equation. So now you have 4+3=7. The last thing left is to verify, you do it to prove that the answer is right and both sides are equal, 7=7.
Distributive Property
You multiply the coefficient with constant, 3x-2. I showed 3 groups of x (the unknown number (variable)) -2 which is -6. Now the constant is -6, making the equation 3x-6=9. You do all the steps for multiplication since the equation is changed into a multiplication one.
Now you follow the multiplication steps. Isolate the variable by adding +6 since you need to get rid of -6. Remember to also do that on your right side. Cancel the constant by putting an X over it. The balanced equation is now 3x=15. You simplify by getting the variable by itself. Cancel the coefficient so you divide it by itself, 3 divided by 3. Also do that to your other side. You are now left with x=5.
You balance by using the value of the variable in the equation, which is 5. You then simplify by doing the first operation, which is multiplication, 3x5=15. So now you have 15-6=9. The last thing you have to do is to verify your answer. You do it to prove that the answer is right and both sides are equal, 9=9.
Modeling
This modeled equation is 2x-2=6
The two red rectangles represent 2x
The two white circles represent -2
The six black circles represent -6
You have to get rid of -2 by adding +2
Remember that whatever you do the left side, you must do to the right
Now you are left with 2x=8 since you added +2 to the right side also
You share the 8 black circles between the 2 red rectangles and you circle the group so you show what each rectangle is worth
Definitions Variable- A variable is a letter or a symbol that will represent a number in the equation.
In this case, the letter "X" is the variable.
Constant- In algebra a constant is a "fixed value," a number on its own in the equation.
In this equation the number "7" and"5" are the constants! Co-efficient- When your number in the equation is being multiplied, divided, added, or subtracted by your variable.
In this equation, the number "5x" is the co-efficient.
Comic!
VIDEOS! In this section Jethro and I explain how to do 2-step multiply, 2-step divide, and also how to verify your answer. :)
