Question

A student simplifies (6b + 4r) – (2b + r) and says that the result is 4b + 5r. Explain the error and describe the correct steps to simplify the expression.

Answer 1

Let's say two students have only books and rulers in their backpacks

If one student has 6 books in their backpack, we can shorten that to saying 6b
b = 1 book
6b = 6 books

If this same student had 4 rulers, then we write 4r
r = 1 ruler
4r = 4 rulers

This leads to the expression 6b+4r indicating 6 books and 4 rulers

The expression (2b+r) means the other student would have 2 books and 1 ruler

(6b+4r) - (2b+r) is what happens when we subtract the two backpacks
Specifically we subtract the number of books together
6 books - 2 books = _____ books
and do the same for the rulers too
2 rulers - 1 ruler = _____ rulers

Or in shorthand we write
6b - 2b = _____
2r - 1r = _____

Answer 2

Hopefully that all makes sense

Answer 3

Yeah, that makes sense jimthompson5910

What i did was:
\[6b + 4r - (2b + r)\]\[ 6b + 4r - 2b - r\]\[(6b - 26) + (4r - r)\]\[ 4b + 3r \]

sooo idk

Answer 4

For some reason I wrote the wrong expression for the rulers portion

I should have said
4 rulers - 1 ruler = _____ rulers
which shortens to
4r - r = ____

Answer 5

you have the correct steps @supie though you wrote 6b-26 instead of 6b-2b

Answer 6

Oh ok thanks bro.

Answer 7

no problem