Answer:
In simplifying the statement "bracket(3x+4y)+5x=8x+4y," the properties used include the distributive property and the additive property of equality.
Explanation:
1. Distributive Property: You distribute the value outside the parentheses (in this case, the value 1) to each term inside the parentheses. For example, bracket(3x+4y) becomes 3x + 4y.
2. Additive Property of Equality: You can add or subtract the same value to both sides of the equation without changing the equality. In this case, you subtract 4y from both sides to simplify the equation.
After applying these properties, the equation simplifies to 3x + 4y + 5x = 8x + 4y.
Now, you can further simplify this equation by combining like terms on both sides. You do this by adding or subtracting the coefficients of the same variables. In this case, you can see that 3x and 5x are like terms on the left side, and 8x and 4y are like terms on the right side. So, you can simplify as follows:
(3x + 5x) + 4y = 8x + 4y.
Combining like terms:
8x + 4y = 8x + 4y.
Now, you can see that the equation simplifies to 8x + 4y = 8x + 4y. At this point, you notice that both sides of the equation are identical. This means that the equation is an identity, which means it's true for all values of x and y. In other words, the equation doesn't have a unique solution; it's always true.