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one number is three more than a second number. Three times the first is 7 less than 2 times the second. Find the numbers.


The value of the second number is ___

  • math -

    second number ---- x
    first number ------ x+3

    A lot of students have difficulty translating an English inequality statement like "Three times the first is 7 less than 2 times the second" into an equation.
    Here is the way I used to teach this: ..

    Re-word the statement as
    "Three times the first is less than 2 times the second by 7"
    now translate that
    3(x+3) < 2(x) by 7
    let's add that difference of 7 to the smaller side, now they would be equal

    3(x+3) + 7 = 2(x)
    3x + 9 + 7 = 2x
    x = -16

    so second number is -16, he first is -13


    check:
    3 times the first = 3(-13) = -39
    2 times the second = 2(-16) = -32

    is -39 7 less than -32 ??? YEAHH!

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