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Please help: simple algebra confusion.

  1. Dec 15, 2007 #1
    I’m currently on working on solving linear equations, and I’m having some trouble understanding whether a minus sign is actually separating two terms, or if it is actually part of the term.

    Here’s something that snagged me, it’s the left member of the equation:

    [tex]\displaystyle{7(2x - 3) - 4(x + 5)}[/tex]

    Regarding the minus sign just before the “4”, should I think of that as “separating” the two terms, or should I think of it as actually being a part of the term, and hence the value is -4?

    I keep wanting to write: [tex]\displaystyle{14x - 21 - 4x + 20}[/tex], but apparently this is false.

    It should be [tex]\displaystyle{14x - 21 - 4x - 20}[/tex]

    I’m just confused, because I clearly remember a rule stating that when subtracting a term, every sign has to change. For example:

    [tex]\displaystyle{(7 - 3) - (2 - 1) = 7 - 3 - 2 + 1}[/tex]

    Any help would be greatly appreciated!
    Last edited: Dec 15, 2007
  2. jcsd
  3. Dec 15, 2007 #2
    [tex]x+5[/tex] can be thought of as one term, so it's the same as if you were multiplying 4 by any regular number or variable. Because it's one term you multiply the whole thing by 4, which gives you [tex]-4x-20[/tex].

    That's how I like to think of it, hope that helped.
  4. Dec 16, 2007 #3


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    Remember now the basic substitution rule:
    Whenever substituting something by means of an identity, you will always get the correct result by setting a parenthesis around the new substitute.

    Thus, since 4(x+5)=4x+20 and 7(2x-3)=14x-21, we may write:

    7(2x-3)-4(x+5)=(14x-21)-(4x+20)=14x-21-4x-20, by removing the parentheses in the correct manner.

    Since substitution with parantheses guarantees you the correct result (assuming you know your identities and how to remove parentheses), a good rule of thumb is always to substitute WITH parenthesis into a "complicated" expression.
    Last edited: Dec 16, 2007
  5. Dec 16, 2007 #4
    Thanks everyone.
  6. Dec 17, 2007 #5
    You could think of it as an operation in subtraction of the qualtity 4(x+5), but the statement can also be written as 7(2x-3) + (-4)(x+5) and consider it addition of signed numbers.
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