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Math Help - Linear Application Question (basic)

  1. #1
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    Linear Application Question (basic)

    Part of the expression in a book reads:
    x+(x + 1) = 25
    which becomes
    2x + 1 = 25

    My question is how does the above expression become 2x+1=25?

    I thought when you see an expression such as x+(x+1) there is a hidden integer, a 1 therefore it should read x+1(x+1)=25. If that is the case shouldn't it be 2x + 2 = 25?

    Obviously I am not understanding it correctly, I just wanted to show my incorrect logic.

    Thanks
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    Re: Linear Application Question (basic)

    Quote Originally Posted by allyourbass2212 View Post
    My question is how does the above expression become 2x+1=25?
    x+(x+1) = 25

    \Rightarrow (x+x) + 1 = 25 (Associativity of addition)

    \Rightarrow x(1+1) + 1 = 25 (Distributive property)

    \Rightarrow x\cdot2 + 1 = 25 (1+1=2)

    \Rightarrow 2x + 1 = 25 (Commutativity of multiplication)

    Normally we wouldn't show all of those steps. In general, to add like terms (terms with the same variables and powers), you add their coefficients. So, for example,

    2x + x = 3x

    a + a + b = 2a + b

    4xy^2 + 3xy^2 = 7xy^2

    Quote Originally Posted by allyourbass2212 View Post
    I thought when you see an expression such as x+(x+1) there is a hidden integer, a 1 therefore it should read x+1(x+1)=25. If that is the case shouldn't it be 2x + 2 = 25?
    Okay, but this "hidden integer" is being multiplied, not added.
    Thanks from allyourbass2212
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