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 subtraction property of equality
B. the addition property of equality
C. the division property of equality
D. the multiplication property of equality
Answer (2)
To solve the equation, we use the addition property of equality. We add 25 to both sides of the equation to isolate the term with x on the left side. The correct answer is B. the addition property of equality.
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 need to determine the justification for step 2.
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. Looking at Step 1, we have 7 x − 25 = 4 x − 1 . To eliminate the − 25 on the left side, we can add 25 to both sides of the equation:
7 x − 25 + 25 = 4 x − 1 + 25
This simplifies to:
7 x = 4 x + 24
Justification Since we added 25 to both sides of the equation, the justification for this step is the addition property of equality.
Final Answer Therefore, the correct answer is B. the addition property of equality.
Examples
The addition property of equality is a fundamental concept in algebra and is used in many real-world applications. For example, if you are balancing a checkbook and you find that you are $25 short, you can add $25 to both sides of the equation to find the correct balance. This property is also used in physics to solve for unknown variables in equations.
The justification for Step 2 is the addition property of equality, as we added 25 to both sides of the equation to isolate the term with x. Therefore, the correct answer is B. the addition property of equality.
;
