Math

1. The sum of a number and 2 is 6 less than twice that number.

2. A rectangular garden has a width that is 8 feet less than twice the length. Find the dimensions if the perimeter is 20 feet.

4. Six times a number is less than 72. What numbers satisfy this condition?

5. A number increased by 10 is greater than 50. What numbers satisfy this condition?

I am confused as to how to convert them into equations. These are not test questions I promise. Can someone please help clear the darkness a little?

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  1. In many of these it is important to see what "verbiage" can be ignored and to key in on the critical phrases.
    e.g. #2
    - "rectangular" is important since we need the perimeter
    - "a width that is 8 feet less than twice the length"
    The reference was "the length", so let the length be x
    I see "twice the length" ----> 2x
    I see "8 feet less than 2x -----> 2x - 8
    I know the perimeter is : twice the length + twice the width
    = 2(x) + 2(2x-8)
    But we are told that equals 20 , so
    2x + 2(2x-8) = 20
    Now just solve that

    let's try another:
    #5 A number increased by 10 is greater than 50.
    " a number" ---- x
    "increased by 10" ---- +10
    "is greater than" ----- >
    x + 10 > 50
    etc

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  2. Simplification

    1.

    x + 2 = 2 x - 6,

    2.

    W = 2 L - 8

    P = 2 ( L + W ) = 2 ( L + 2 L - 8 ) = 2 ( 3 L - 8 ) = 6 L - 16 = 20

    6 L -16 = 20

    4.

    6 x < 72

    5.

    x + 10 > 50

    Try to solve this equations.

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  3. Looking at #1,
    -- The sum of a number and 2 is 6 less than twice that number --

    Some students find this type of problem confusing. Do I add or subtract that 6?
    I know there is a < somewhere.

    I suggested that they rephrase the problem:
    "The sum of a number and 2 is less than twice that number by 6 "
    x + 2 < 2x by 6
    so right now the 2x is the bigger part by 6
    so if we subtract 6 from the right side, they would be equal, so
    x + 2 = 2x - 6
    x = 8

    check:
    the sum of the number and 2 : 8 + 2 = 10
    twice the number: 16
    is 10 less than 16 by 6 ? YES

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