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Math Help - finding x

  1. #1
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    finding x

    2(3x + 4) = 4x + 16 find x


    2y = 1/2(3y + 5) find y


    d + 2 = 1/2(4d - 6) find d


    4q - 2 = 2(3q - 6) find q


    Can someone offer help?
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  2. #2
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    e^(i*pi)'s Avatar
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    The Distributive law is used here. Can you expand the brackets?
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  3. #3
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    Expand the brackets?
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  4. #4
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    You should know that \displaystyle a(b + c) = ab + ac. See how what's on the outside has been multiplied by everything on the inside?

    If you do that then that simplifies the problems greatly.

    This is called "expanding the brackets".
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  5. #5
    Super Member bigwave's Avatar
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    Quote Originally Posted by tysonrss View Post
    2(3x + 4) = 4x + 16 find x
    as mentioned your first step should look like this

    6x + 8 = 4x +16

    it easy from here

    expanding the brackets means distribution
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  6. #6
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    If the distributive law is not desired then as a first step for each

    Q1. divide both sides by 2

    Q2. times both sides by 2

    Q3. times both sides by 2

    Q1. divide both sides by 2
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  7. #7
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    Quote Originally Posted by pickslides View Post
    If the distributive law is not desired then as a first step for each

    Q1. divide both sides by 2

    Q2. times both sides by 2

    Q3. times both sides by 2

    Q1. divide both sides by 2
    Even after doing this, you will still need to expand some brackets...
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  8. #8
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    Quote Originally Posted by tysonrss View Post
    2(3x + 4) = 4x + 16 find x
    The idea of these problems is to get all of the unknown(in this case x) on one side and the numbers on the other.
    Firstly , expand all the brackets.
    This can be done by multiplying 2(the factor) into the bracket.
    = 6x + 8 (nothing changes on the right side)
    6x + 8 = 4x + 16
    Now, 'move' the x to the left side and the 8 to the right side.
    Subtract 8 and 4x from both sides.
    6x +8 - 8 - 4x = 4x - 4x -8 + 16
    2x =  8
    x = \dfrac{8}{2} = 4.

    Solve the other problems in the similar fashion. Hope this helps.
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