SOLUTION: Find a number that is 68 greater than three times its opposite

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Question 1045726: Find a number that is 68 greater than three times its opposite

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
an opposite number has the same magnitude, but the opposite sign.

68 is opposite -68

68 is the same distance from 0 that -68 is.

that makes them opposite numbers by definition.

let x be the number.

your equation would be:

x = 3 * -x + 68

this can be re-written as:

x = -3x + 68

this is based on the commutative law of multiplication and the associative law of multiplication.

the commutative law says that a * b = b * a

the associative law says that a * (b * c) = (a * b) * c

x = 3 * -x + 68 becomes x = 3 * -1 * x + 68 which becomes x = -1 * 3 * x + 68 which becomes x = (-1 * 3) * x + 68 which becomes x = -3 * x + 68 which becomes x = -3x + 68.

here's a reference to the different laws / properties of arithmetic operations.

http://www.coolmath.com/prealgebra/06-properties