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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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What do you think the answer is?
  • phi
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 ?

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Other answers:

that would mean there are 30 3x's and 10 -1's ?
  • phi
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)
  • phi
in other words 10(3x -1) is 30x + -10 which can be written 30x-10
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! :)
  • phi
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)
  • phi
the answer to this problem is mistake was to not multiply both terms by the "factor"
ohh so they did not properly distibute the whole problem?
  • phi
yes, they did 10(3x-1) --> 10*3x -1 which means they did not do 10*-1
I know, that is what I meant, I just did not know how to word it xD
Thank you Phi ! you really helped me !
  • phi
you said it ok
  • phi
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)
okay! thank you for such a thorough explanation and not just giving out answers!

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