Martinez Paul
10/23/2023 · Middle School
C. The same nonzero real number may multiply both sides of an equation without changing the equation's solution set, so \( a=b \) and \( a c=b c \) are equivalent equations as long as \( c \neq 0 \). Dolution set, so \( a=b \) and \( a c=b c \) are equivalent equations. shoose the correct example of the multiplication property of equality below. A. The equations \( x=3 \) and \( x+2=5 \) are equivalent. B. The equations \( x=3 \) and \( x+2=6 \) are equivalent. C. The equations \( x=3 \) and \( 2 x=5 \) are equivalent. D. The equations \( x=3 \) and \( 2 x=6 \) are equivalent.
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Step-by-step Solution
To identify the correct example of the multiplication property of equality, we need to find an example where both sides of an equation are multiplied by the same nonzero number, and the resulting equations remain equivalent.
Let's analyze the options:
A. The equations \( x=3 \) and \( x+2=5 \) are equivalent.
- This is not an example of the multiplication property of equality.
B. The equations \( x=3 \) and \( x+2=6 \) are equivalent.
- This is also not an example of the multiplication property of equality.
C. The equations \( x=3 \) and \( 2x=5 \) are equivalent.
- This is not an example of the multiplication property of equality, as \( 2x=5 \) does not result from multiplying \( x=3 \) by a nonzero number.
D. The equations \( x=3 \) and \( 2x=6 \) are equivalent.
- This is an example of the multiplication property of equality. If we take the equation \( x=3 \) and multiply both sides by 2, we get \( 2x=6 \), which is equivalent to the original equation.
Therefore, the correct answer is:
**D. The equations \( x=3 \) and \( 2x=6 \) are equivalent.**
Quick Answer
The correct example is D. The equations \( x=3 \) and \( 2x=6 \) are equivalent.
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