Select the correct answer.
Simon used these steps to solve an equation:
Step 1: $-6(x+7)=2(x-11)$
Step 2: $-6 x-42=2 x-22$
Step 3: $-8 x-42=-22$
Step 4: $-8 x=20$
Which property did he use to get from step 3 to step $4 ?$
A. addition property of equality
B. distributive property
C. subtraction property of equality
D. transitive property
Answer (1)
To isolate the term with x in step 3, add 42 to both sides of the equation.
This operation uses the addition property of equality.
Therefore, the correct answer is A.
The property used to get from step 3 to step 4 is the addition property of equality: A .
Explanation
Understanding the Problem We are given the equation − 6 ( x + 7 ) = 2 ( x − 11 ) and the steps Simon used to solve it. We need to determine which property was used to get from step 3 to step 4.
Listing the Steps Step 1: − 6 ( x + 7 ) = 2 ( x − 11 )
Step 2: − 6 x − 42 = 2 x − 22
Step 3: − 8 x − 42 = − 22
Step 4: − 8 x = 20
Isolating the x Term To get from step 3 ( − 8 x − 42 = − 22 ) to step 4 ( − 8 x = 20 ), we need to isolate the term with x . This means we need to get rid of the − 42 on the left side of the equation. To do this, we add 42 to both sides of the equation: − 8 x − 42 + 42 = − 22 + 42
− 8 x = 20
Identifying the Property The property that allows us to add the same value to both sides of an equation without changing the equality is 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 budget and need to add an unexpected expense, you must also add an equal amount to your income or reduce another expense to maintain the balance. Similarly, in physics, when analyzing forces acting on an object, if you add a force in one direction, you must add an equal and opposite force to maintain equilibrium. Understanding and applying the addition property of equality ensures that equations remain balanced and accurate in various mathematical and practical contexts.
