Chap 5 Algebra: 6 A.M. QUIZ (23 May 2010) (II)

Explain, with examples:
Which is larger: 2+n or 2n?

Note: This is a 6-mark question.

7 comments:

  1. This comment has been removed by the author.

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  2. The answer varies.

    For example, if n's value is 1, 2+n would be larger than 2n as 2+n would have a value of 3 while 2n would only have a value of 2.

    If the value of n were 2, 2+n and 2n would be of equal values as both would have a value of 4.

    If the value of n were 3, 2n would be larger than 2+n as 2n would have a value of 6 while 2+n would only have a value of five. This also applies if the value of n is more than 3.

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  3. The answer depends on n, which means it varies.

    If the value of n is 1 or below, 2+n would be larger than 2 x n.
    Eg. n = 0.5,
    2 + 0.5 = 2.5
    2 x 0.5 = 1
    2.5 is bigger than 1, which means 2+n is larger than 2 x n.

    If the value of n is 2, 2 + n would be equal to 2 x n.
    n = 2,
    2 + 2 = 4
    2 x 2 = 4
    4 = 4, which means 2 + n would be equal to 2 x n.

    If the value of n is more than 2, 2n would be larger than 2 +n.
    eg. n = 2.2
    2 + 2.2 = 4.2
    2 x 2.2 = 4.4
    4.4 is bigger than 4.2, which means that 2 x n is bigger than 2 + n.

    JJ(:

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  4. 2n is larger then 2 + n

    First, the answer will depend largely on the variable (n).
    Second, the constant is 2 in both equations.

    If the variable is 1 or 0 , 2n will be smaller then 2 +n since 2n= 2 x 1 or 2 x 0 and 2 +n is 2 + 1 or 2 + 0.

    If the variable is 2 , there will be the same answer as 2 x 2= 4 and 2 + 2= 4

    If the variable is more than 2, 2n will always be larger than 2 +n since there are 2 groups of the variable and 2 + 1 group is always smaller when the variable is more than 2.

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  5. 2n is larger.
    Why?
    2n is 2 x n, which is multiple, but 2+n is addition.
    for example n=4
    2+4=6, but 2x4=6

    2+n can also be larger.
    As long as the variable is no larger than the constant, 2+n is larger.
    Example:

    n=1:
    2+1=3
    2x1=2

    n=(-1):
    2+(-1)=1
    2x(-1)=-2

    Therefore, I can conclude that the answer cannot be defined as both answers are correct unless more information is provided like the value of n, the constant.

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  6. The answer varies.

    If n < 3, then 2+n is greater than 2n.

    For example, n = 1,
    then 2 + 1 = 3,
    and 2 x 1 = 2,
    from here we can see that 2+n is greater than 2n.

    If n > 3, or n = 3, then 2n is greater than 2+n.

    For example, n = 4,
    then 2 + 4 = 6,
    and 2 x 4 = 8,
    from here we can see that 2n is greater than 2+n.

    Therefore, we can only decide whether 2+n or 2n is greater when we are given the value of "n".

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  7. It depends on the value of the variable 'n'.
    For example, if n=1.
    2+1=3
    2x1=2
    This time, 2+n is greater than 2n.

    For example, if n=2.
    2+2=4
    2x2=4
    This time, 2+n and 2n is the same.

    However, if n=3 and above, 2n will be greater than 2+n.

    Hence, it depends on the value of 'n'.

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