what is the result when you add 0 to both sides of an equation?
I asked this already, but I would like a deeper explination
0 is the additive identity. So, by definition.
x+0 = 0
Then there is what is commonly called the additive property of equality:
equals added to equals are equal.
That is, if you have
x = x
then x+y = x+y
So, if y=0, x+0 = x+0 ... x=x
When 0 is added, nothing changes.
When you add 0 to both sides of an equation, the result is that the equation remains unchanged. In simpler terms, adding 0 to both sides does not affect the equality between the two sides of the equation.
To understand why this happens, let's take a step-by-step approach:
1. An equation shows a balance between two expressions or quantities. For example, consider the equation: 2x + 3 = 7.
2. Adding 0 to both sides entails adding nothing to the equation; it's like introducing a placeholder. Mathematically, the equation becomes: 2x + 3 + 0 = 7 + 0.
3. When you simplify the equation after adding 0, you get the same original equation: 2x + 3 = 7.
This happens because adding 0 to any number does not change its value. It is a property of addition called the "Additive Identity Property," which states that adding 0 to any number results in the same number.
Now, you might wonder, why would you add 0 to both sides of an equation if it doesn't change anything? Well, there are situations where adding 0 can be useful in solving more complex equations, especially when you want to isolate a variable or manipulate the equation algebraically.
In summary, adding 0 to both sides of an equation leaves the equation unchanged. Although it might seem redundant, it can be a helpful algebraic technique when working with more complicated equations.