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Answer :
To solve the problem, let's break it down step-by-step:
1. Understand the Equation: You are given the equation [tex]\( JK + LM = NP + LM \)[/tex].
2. Objective: We want to figure out how we can simplify this equation to show that [tex]\( JK = NP \)[/tex].
3. Simplify the Equation:
- Notice that [tex]\( LM \)[/tex] is added to both sides of the equation.
- To isolate [tex]\( JK \)[/tex] and show that it equals [tex]\( NP \)[/tex], we need to eliminate [tex]\( LM \)[/tex] from both sides.
4. Apply the Property:
- You can subtract [tex]\( LM \)[/tex] from both sides of the equation. This operation will maintain the equality and is known as the Subtraction Property of Equality. It states that if you subtract the same value from both sides of an equation, both sides remain equal.
- So, subtract [tex]\( LM \)[/tex] from both sides:
[tex]\[
(JK + LM) - LM = (NP + LM) - LM
\][/tex]
- This simplifies to:
[tex]\[
JK = NP
\][/tex]
5. Conclusion:
- By subtracting [tex]\( LM \)[/tex] from both sides, we used the Subtraction Property of Equality to prove that [tex]\( JK = NP \)[/tex].
Therefore, the correct answer here is D. Subtraction Property.
1. Understand the Equation: You are given the equation [tex]\( JK + LM = NP + LM \)[/tex].
2. Objective: We want to figure out how we can simplify this equation to show that [tex]\( JK = NP \)[/tex].
3. Simplify the Equation:
- Notice that [tex]\( LM \)[/tex] is added to both sides of the equation.
- To isolate [tex]\( JK \)[/tex] and show that it equals [tex]\( NP \)[/tex], we need to eliminate [tex]\( LM \)[/tex] from both sides.
4. Apply the Property:
- You can subtract [tex]\( LM \)[/tex] from both sides of the equation. This operation will maintain the equality and is known as the Subtraction Property of Equality. It states that if you subtract the same value from both sides of an equation, both sides remain equal.
- So, subtract [tex]\( LM \)[/tex] from both sides:
[tex]\[
(JK + LM) - LM = (NP + LM) - LM
\][/tex]
- This simplifies to:
[tex]\[
JK = NP
\][/tex]
5. Conclusion:
- By subtracting [tex]\( LM \)[/tex] from both sides, we used the Subtraction Property of Equality to prove that [tex]\( JK = NP \)[/tex].
Therefore, the correct answer here is D. Subtraction Property.
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