twice the sum of a number and 5 is equal to three times the difference of the number and 7

Question

I don't know how to put my word problem into a format.

Answer 1

2(n + 5) = 3(n - 7)

 

Solve for n.

Answer 2

Translating the words can be hard.
First, what are quantities the problem is interested in? It looks like there is “a number”. So let’s translate that as “x”.
Next, what formula is related to that number? It’s complicated, so let’s piece it together. First off, there’s an “equals”, so
(Stuff on the left) = (stuff on the right)
Then what is the stuff on the left?
“Twice the sum of a number and 5”. We have a name for “a number”, so we can write this as
“Twice the sum of x and 5”
Now translate “sum of x and 5” into “x+5”
“Twice (x+5)”
What does “Twice” mean? It means “2 times”
“2*(x+5)”—this is the “stuff on the left”
Now for the stuff on the right.
“three times the difference of the number and 7”
Once again, we have a name for “a number”, “x”
“Three times the difference of x and 7”
Now you need to know that “difference of x and 7” means subtraction.
“Three times (x - 7)”
Finally, you know that “times” means “multiply”.

“3*(x-7)”. This is the stuff on the right.
Now the translation is complete
2*(x+5) = 3*(x-7)

I assume that you know how to solve this for x. But I’ll complete the solution
First multiply out
2x + 10 = 3x - 21
Now collect terms
10 + 21 = 3x - 2x
Simplify
31 = x