To fill in the missing justifications in the correct order, let’s analyze the steps in the mathematical statement provided:
- 4x + 3 = x + 5 − 2x - This is the original equation (Given).
- 4x + 3 = x − 2x + 5 - Here, the justification is the Commutative Property of Addition as it allows us to rearrange the terms on the right side.
- 4x + 3 = -x + 5 - This is combining like terms on the right side. Therefore, the justification is Combine Like Terms.
- 5x + 3 = 5 - To isolate the variable term, we apply the Addition Property of Equality by adding x to both sides.
- 5x = 2 - This step appears incorrect; actually, it should be 5x = 5 - 3. The justification used here would be the Subtraction Property of Equality.
- x = two fifths - To solve for x, we divide both sides by 5, thus using the Division Property of Equality.
Let's recap the suitable order of justifications:
- Given
- Commutative Property of Addition
- Combine Like Terms
- Subtraction Property of Equality
- Division Property of Equality
As a result, option 2 fits correctly when considering the explanations laid out:
Combine Like Terms; Addition Property of Equality; Subtraction Property of Equality; Division Property of Equality
It's important to note that the steps listed in the original problem and the justifications may not align directly with the final answer, so careful attention should be given to each action taken on the equation.
In the context of the answer choices provided, the closest items that may apply are:
Combine Like Terms; Subtraction Property of Equality; Addition Property of Equality; Division Property of Equality.
If you need further assistance clarifying any particular step, please let me know!