I'm not really sure on how to prove statements are right with properties as reasons. How would you solve this?
If x + c = 0, then x = -c
Statements:
1. x+c=0
2. (x+c)+(-c) = 0 + (-c)
3. x + [c+(-c)] = 0 + (-c)
4. x + 0 = 0 + (-c)
5. x = (-c)
Would 5 be the substitution property?
Does that mean 1 would be be reasoned by the substitution property?
yes i think that's correct coz when we do this sum ,,,we do it in this way
x+c=0
x+c=0
-c -c (subtracting x both side)
-------
that is x=-c
Oh, thank you. For number 2, I originally had the definition of addition, but I was marked wrong. I'm not very sure, but wouldn't it be considered the definition of addition if you were adding (-c) to both sides? And also, in this case x+c would equal 0 so that would be the reason you are substituting 0 for x+c in number 2 as well. I don't really understand properties..
yes that's it/......u got it
Yes, Statement 5 would be an application of the Substitution Property.
To prove that the statement "If x + c = 0, then x = -c" is true using properties as reasons, you need to show a step-by-step logical progression of equations, using various properties of equality.
Let's go through each statement and explain how to reach it:
Statement 1: x + c = 0
This is the given equation.
Statement 2: (x + c) + (-c) = 0 + (-c)
In this step, you are subtracting c from both sides of the equation to isolate x. This is an application of the Addition Property of Equality.
Statement 3: x + [c + (-c)] = 0 + (-c)
Here, you are using the Associative Property of Addition to rearrange the terms (c + (-c)).
Statement 4: x + 0 = 0 + (-c)
Using the Additive Inverse Property, you replace the expression (c + (-c)) with 0.
Statement 5: x = (-c)
Finally, the Substitution Property is applied here to replace the expression "0 + (-c)" with "-c". This step shows that if x + c = 0, then x can be substituted with -c.
So, by using these properties of equality, you have successfully proven that if x + c = 0, then x = -c.