841 Math Blog

Script:
Detective Brooks: Hello there, I'm Detective Brooks.
Lorie: Hello, I'm Lorie.
Detective Brooks: I see you're doing some kind of paper work.
Lorie: Yes, it's my homework! Have you heard of it?
Detective Brooks: Of course I have. What kind of homework is it?
Lorie: Combining like terms and distributive property.
Detective Brooks: Oh, I see. I was really good at that when I was in school.
Lorie: Really. *sarcastically*
Detective Brooks: I was, I probably still am. I can solve anything, well almost anything. What's the question?
Lorie: Sure you are. The question is n+3-5n+12.
Detective Brooks: Why don't you try and solve it, then I'll check if you're right.
Lorie: Alright then.
Lorie: My answer is -6+15.
Detective Brooks: Well it looks to me that you're wrong!
Lorie: That's impossible!
Detective Brooks: It's possible.
Lorie: If you're so good at this, why don't you tell me where I went wrong?
Detective Brooks: I will.
Detective Brooks: First combine like terms and remember to look at the operation sign. n-5n=-4 and 3+12=15. Therefore, the answer is -4+15. Do you see where you went wrong?
Lorie: Yes, now I see my mistake. I combined 5n and n, I've forgotten 5n was negative.
Detective Brooks: Now you understand, try and solve this question. 2 + 4(3n+8), what do you think the answer is?
Lorie: I think it might be 12n+10.
Detective Brooks: I'm sorry, but your answer is incorrect. First multiply the number closest to the bracket, which is 4. Multiply it to the first number in between the brackets, 3n. 4x3n=12n. Now multiply 4 to the second number, 8. 4x8=32. The question should now be 2+12n+32, all I have to do is combine like terms. 2+32=34, the question simplified is 12n+34!
Lorie: Oh, I'll try to remember that! I'm beginning to understand algebra.
Detective Brooks: That's good, do you know where you made your mistake?
Lorie: Yes, I didn't multiply 4 and 8 together. I just multiplied 4 to 3n and got 12n. After, I added 2 and 8, then I came up with 12n+10.
Detective Brooks: Don't worry, you'll get better and solve it like a mystery!
Lorie: Thank you for your help Detective Brooks, I really needed it! You're a really great detective!
Detective Brooks: Thank you Lorie, you're not so bad yourself!

Chapter Three: One Step Equation Solving

Additive:

The additive equation that I am going to explain how to solve is n+3=5. The first step is to isolate the variable. Then you add the opposite and cancel them out because they are zero pairs. Second, you balance it out by doing the same thing to the other side. So, your left with n=2. So after solving the equation, you have to verify! The first thing you do is rewrite the equation. Second, you replace the variable with the answer you got. The last step is to write down 5=5 to show that you are done.

Subtractive:

The subtractive equation that I am going to explain how to solve is 5-n=3. The first step is to isolate the variable. Second, you add the opposite, which is -5 to +5. Then you cancel them out because they are zero pairs. Third, you balance it out by doing the same thing to the other. So, you subtract 3 from negative 5 and now you are left with n= -2. Then you have to verify! You first need to rewrite the equation. Second, you replace the variable with the answer you got. Last but not least you write down 3=3 to finish it off!

Multiplicative:

The equation that I would explain how to solve is 5n=10. The first step is to isolate the variable. Then you add the opposite by dividing 5 by 5. Second, you need to balance it out by doing the same thing to the other side. So, you are left with the answer n=2 Next you need to verify! You first need to rewrite the equation. Second, you replace the variable with the answer you got which is 5 (2) = 10. Last but not least you write down 10=10 to finish it off!

Divisive:

The equation that I would explain how to solve is n/2=4. The first step is to isolate the variable. Then you add the opposite by dividing 2 by 2. Second, you balance it out by doing the same thing to the other side. Third, you need to verify! You first need to rewrite the equation. Second, you replace the variable with the answer you got. Last but not least you write down 4=4 to finish it off.

This is a video Carrie and I made on how to solve an additive equation, a subtractive equation, a multiplicative equation, and a divisive equation.