Final answer:
To simplify the expression 5x - 3x - 4y + 1/3(6x - 12y), combine like terms and distribute the coefficient, resulting in the expression 4x - 8y. This expression cannot be further factored. The expressions 4x - 8y and 5x - 3x - 4y + 1/3(6x - 12y) are equivalent because we followed the rules of algebra in simplifying the expression.
Step-by-step explanation:
To simplify the expression 5x - 3x - 4y + 1/3(6x - 12y), we can first combine like terms. 5x - 3x = 2x. So the expression becomes 2x - 4y + 1/3(6x - 12y). Next, we distribute the 1/3 to the terms inside the parentheses. 1/3 * 6x = 2x and 1/3 * -12y = -4y. So the expression now becomes 2x - 4y + 2x - 4y. We can then combine like terms again. 2x + 2x = 4x and -4y - 4y = -8y. Therefore, the simplified expression is 4x - 8y.
To express this answer in factored form, we cannot factor out any common factors. So the expression remains as 4x - 8y.
We know that the expressions 4x - 8y and 5x - 3x - 4y + 1/3(6x - 12y) are equivalent because we followed the rules of algebra to simplify the expression. We combined like terms and distributed the coefficient outside the parentheses to each term inside. By performing these operations correctly, we arrived at the same final expression.