If 10a = 2b and 2b = c, then 10a = c.
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1 point
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Distributive Property
Substitution Property
Reflexive Property
Symmetric Property
Transitive Property
Transitive Property
The correct answer is the Transitive Property.
The Transitive Property states that if a = b and b = c, then a = c. In this case, we are given that 10a = 2b and 2b = c. By applying the Transitive Property, we can conclude that 10a = c.
The correct answer is the Transitive Property.
To understand why, let's break down the equation step by step:
1. Given: 10a = 2b, and 2b = c
To prove that 10a = c, we can use the Transitive Property, which states that if a=b and b=c, then a=c.
2. From 10a = 2b, we can divide both sides by 10 to solve for a:
(10a)/10 = (2b)/10
Simplifying, we get:
a = b/5
3. Now, substitute the value of b from the second equation (2b = c) into our expression for a:
a = (2b)/5
Since 2b is equal to c, we can write:
a = c/5
4. Finally, multiply both sides of the equation by 10 to get 10a = c:
10a = 10 * (c/5)
Simplifying, we have:
10a = 2c
Therefore, by using the Transitive Property, we have proven that if 10a = 2b and 2b = c, then 10a = c.