It seems you are asking about the process of demonstrating that two algebraic expressions are equivalent and providing a specific equation as an example. Based on the steps you've mentioned, let’s analyze the equation step by step and clarify the explanation.
You’ve provided the equation:
\[ 12a + 10 + 8 = 10 + 8 + 12a \]
Step 1: Simplifying the Expression
First, simplify both sides of the equation:
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On the left side: \[ 12a + 10 + 8 = 12a + 18 \]
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On the right side: \[ 10 + 8 + 12a = 18 + 12a \]
So, we can rewrite the original equation as:
\[ 12a + 18 = 18 + 12a \]
Step 2: Recognizing the Equivalence
Here, you can see that both sides of the equation are actually the same. This shows that:
\[ 12a + 18 = 18 + 12a \]
Step 3: Conclusion
You can conclude that the expressions are equivalent because they simplify to the same expression. In algebra, both sides of the equation represent the same value for any value of \( a \).
Clarification of the Second Equation
You mentioned another expression:
\[ 10 + 13a = 10 + 13a \]
This equality is trivially true as both sides are identical. It serves as another example of equivalent expressions.
Summary
To find missing steps in your reasoning or to prove equivalency, always simplify both sides of the equation, and check whether they are the same. In this case, both presented equations confirm that they are indeed equivalent expressions.