I'm on the topic of "Algebra proofs".
Is this statement an example of a transitive property?: If CD=AB and AB=8 then CD=8
Here's another problem I want you to check& note that I only have 4 blanks per side of the table (statements and reasons)
Given: 2(x+3)=3x+1
Prove: 5=x
Statement Reasons
2(x+3)=3x+1 Given
2x+6=3x+1 Distributive
5=1x Subtraction&subtraction
5=x Division
transitive yes
the proof looks ok, too
faction in simple form
The statement "If CD=AB and AB=8, then CD=8" is indeed an example of the transitive property of equality. The transitive property states that if two quantities are equal to the same quantity, then they are also equal to each other.
To prove the equation "5=x" using the given equation "2(x+3)=3x+1", you can follow the steps below:
Statement | Reasons
---------------------------------------------------------
2(x+3) = 3x+1 | Given
2x+6 = 3x+1 | Distributive property
2x+6-3x = 3x+1-3x | Subtract 3x from both sides
-x+6 = 1 | Simplify the equation
6-1 = x | Add x to both sides
5 = x | Simplify further
During these steps, we used the distributive property to simplify the equation. Then, we subtracted 3x from both sides to isolate the x term on one side of the equation. After simplifying, we added x to both sides to isolate x as a single term, resulting in the conclusion that "5=x."