Kathleen's Algebra Unproject

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*