Lin and Noah are solving the equation 7(x+2)=91.
Lin starts by using the distributive property. Noah starts by dividing each side by 7.
Show what Lin's and Noah's full solution methods might look like.
What is the same and what is different about their methods?
I know the answer to Noah's, but I'm not very good with distributive property, so I'll refrain from explaining Lin's.
The equation we are given is 7(x+2)=91. To simplify this, and solve it, we need to single out the x and it's value. So, with that logic, we have to get rid of all the other junk.
To do this, you have to cancel out the other numbers. You first start off with what's on the outside of the parentheses.
7(x+2)=91
÷7 ÷7
x+2=91
You see? You had to do the opposite of what the equation tells you to do. Dividing the 7, and the 91 both by 7 will cancel ot
Lin: 7x+14 = 91
Noah: x+2 = 13
...
-cancel it out. I'm afraid I accidentally clicked post. Anyways, now we have x+2=13 (Apologies on this too, I misclicked).
x+2=13
...-2....-2
x=11
And there, you've solved it. :)
i could figure out noahs, it is X = 11
Lin's method:
Lin starts by using the distributive property to simplify the equation. The distributive property states that if you have a number outside parentheses multiplying with a sum inside the parentheses, you can distribute the multiplication to each term inside the parentheses. In this case, Lin multiplies 7 with both x and 2:
7(x+2) = 7*x + 7*2 = 7x + 14
Now, Lin has simplified the left side of the equation.
Next, Lin sets the simplified equation equal to 91:
7x + 14 = 91
To solve for x, Lin subtracts 14 from both sides of the equation to isolate the term with x:
7x + 14 - 14 = 91 - 14
7x = 77
To get the value of x, Lin divides both sides of the equation by 7:
7x/7 = 77/7
x = 11
Therefore, the solution to the equation 7(x+2) = 91 using Lin's method is x = 11.
Noah's method:
Noah starts by dividing each side of the equation by 7 to isolate the term with x:
7(x+2)/7 = 91/7
x + 2 = 13
Next, Noah subtracts 2 from both sides of the equation:
x + 2 - 2 = 13 - 2
x = 11
Therefore, the solution to the equation 7(x+2) = 91 using Noah's method is also x = 11.
What is the same and what is different about their methods?
Both Lin and Noah arrived at the same solution, which is x = 11. They both correctly solved the equation.
However, the methods they used were different. Lin used the distributive property to simplify the equation before solving for x, while Noah directly divided each side of the equation by 7 to isolate the term with x. Lin's method involved more steps but provided a clearer visual representation of how the equation was simplified. Noah's method was faster but relied more on mental calculations. Both methods are valid approaches to solving the equation, but they differ in terms of the techniques used.
The thing that is the same about the methods is: they both used mathematical means to solve.
What is different is: Lin made his equation bigger by using the distributive property, while Noah made his simpler by dividing each piece by 7