Select the correct answer.
What is the justification for step 2 in the solution process?
[tex]$10 x-25-3 x=4 x-1$[/tex]
Step 1: [tex]$7 x-25=4 x-1$[/tex]
Step 2: [tex]$7 x=4 x+24$[/tex]
A. the addition property of equality
B. the division property of equality
C. the subtraction property of equality
D. the multiplication property of equality
Answer (2)
Start with the equation 7 x − 25 = 4 x − 1 .
Add 25 to both sides of the equation: 7 x − 25 + 25 = 4 x − 1 + 25 .
Simplify the equation to get 7 x = 4 x + 24 .
The justification for this step is the addition property of equality, so the answer is A .
Explanation
Understanding the Problem We are given the equation 10 x − 25 − 3 x = 4 x − 1 and the following steps:
Step 1: 7 x − 25 = 4 x − 1 Step 2: 7 x = 4 x + 24
We want to determine the justification for the step from 7 x − 25 = 4 x − 1 to 7 x = 4 x + 24 .
Isolating the x term To get from Step 1 to Step 2, we need to isolate the term with x on the left side of the equation. We can do this by adding 25 to both sides of the equation:
7 x − 25 + 25 = 4 x − 1 + 25
7 x = 4 x + 24
Applying the Addition Property of Equality The addition property of equality states that if you add the same value to both sides of an equation, the equation remains equal. In this case, we added 25 to both sides of the equation. Therefore, the justification for step 2 is the addition property of equality.
Final Answer The correct answer is A. the addition property of equality.
Examples
The addition property of equality is a fundamental concept in algebra that allows us to manipulate equations while maintaining their balance. For example, if you have a simple balance scale with an unknown weight on one side and a known weight on the other, the addition property of equality allows you to add or remove the same amount of weight from both sides without disturbing the balance. This principle is used in various real-life scenarios, such as balancing budgets, calculating ingredient quantities in recipes, and determining the forces acting on an object in physics. Understanding and applying the addition property of equality is crucial for solving equations and making informed decisions in everyday situations.
The justification for Step 2, where we move from 7 x − 25 = 4 x − 1 to 7 x = 4 x + 24 , is based on the addition property of equality, which allows us to add 25 to both sides of the equation. Thus, the correct answer is A. the addition property of equality.
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