Question

Help! I am confused as to how to work this out, much less where her error was made!

Answer 1

What do you think the answer is?

Answer 2

think of the parens as a package
10( 3x -1) means you have 10 "packages" of 3x-1
if you have 10 of (3x-1)
how many 3x's do you have ?
how many -1's do you have ?

Answer 3

that would mean there are 30 3x's and 10 -1's ?

Answer 4

you would have 10 3x's and 10 of -1's
we show that by multiplying: 10*3x + 10* -1
(3x means 3*x, and 10*3*x is the same as 30*x or 30x)

Answer 5

in other words
10(3x -1) is 30x + -10 which can be written 30x-10

Answer 6

Yes, I understand that! (I am great at problems like this, ive just never seen them set up in this particular form before?? ) continue, i am writing all of this down! :)

Answer 7

you will use this "rule" a lot. (called distributive law)
you will also use it backwards,i.e. be able to undo the multiply
and change 30x -10 to 10(3x-1)

Answer 8

the answer to this problem is
mistake was to not multiply both terms by the "factor"

Answer 9

ohh so they did not properly distibute the whole problem?

Answer 10

yes, they did
10(3x-1) --> 10*3x -1
which means they did not do 10*-1

Answer 11

I know, that is what I meant, I just did not know how to word it xD

Answer 12

Thank you Phi ! you really helped me !

Answer 13

you said it ok

Answer 14

I would say "they did not distribute the 10"
it is the number out front (the 10), which they called the "factor" which is "distributed"

in English, distribute means "hand out" so you can think of the 10 as being "handed out" to each term inside the parens. (of course you have to remember you multiply 10 times each term)

Answer 15

okay! thank you for such a thorough explanation and not just giving out answers!