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18 August, 13:09

three times the sum of a number and - 5 equals - 6 times the sum of the number and - 2. Find the number.

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  1. 18 August, 13:32
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    3 (x-5) = -6 (x-2)

    3x-15=-6x+12

    9x-15=12

    9x=27

    x=3
  2. 18 August, 13:38
    0
    "Three times the sum of a number and - 5" - let the number be x.

    "times" indicates multiplication, and "sum" indicates addition. Ignore the "times" part first; that leaves you with "the sum of a number and - 5," which is x + (-5) or x - 5. Now include the multiplication bit, and you get 3 (x - 5). This will be equal to "-6 times the sum of the number and - 2." Similarly, the sum of the two numbers will be multiplied by the first number, - 6. You get - 6 (x - 2). Now you have:

    3 (x - 5) = - 6 (x - 2)

    Solve. Apply the Distributive Property: a (b + c) = ab + ac.

    3 (x - 5) = - 6 (x - 2)

    3x - 15 = - 6x + 12

    Add 15 to both sides to get rid of the constant on the left side of the equation.

    3x - 15 = - 6x + 12

    3x - 15 + 15 = - 6x + 12 + 15

    3x = - 6x + 27

    Add 6x to both sides to get rid of the variable term on the right side of the equation.

    3x = - 6x + 27

    3x + 6x = - 6x + 27 + 6x

    9x = 27

    Divide both sides by 9 to isolate x.

    9x = 27

    9x/9 = 27/9

    x = 3

    Answer:

    The number is 3.
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