Select all of the equations below that are equivalent to: $\newline$ $12g = 8$ $\newline$ Use properties of equality. $\newline$ $\newline$ Multi-select Choices: $\newline$ (A) $12g - 3 = 4$ $\newline$ (B) $12g - 2 = 7$ $\newline$ (C) $12g - 3 = 5$ $\newline$ (D) $12g - 4 = 2$

Full solution

Q. Select all of the equations below that are equivalent to:

\newline

12g = 8

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Use properties of equality.

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\newline

Multi-select Choices:

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(A)

12g - 3 = 4

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(B)

12g - 2 = 7

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(C)

12g - 3 = 5

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(D)

12g - 4 = 2

Understand Equation: Understand the original equation. $\newline$ The original equation is $12g = 8$ . We need to find which of the given choices are equivalent to this equation by using properties of equality.
Check Choice (A): Analyze choice (A) $12g − 3 = 4$ . To check if this is equivalent to the original equation, we can add $3$ to both sides of choice (A) to see if we get the original equation. $12g − 3 + 3 = 4 + 3$ $12g = 7$ This is not equivalent to the original equation $12g = 8$ .
Check Choice (B): Analyze choice (B) $12g − 2 = 7$ . To check if this is equivalent to the original equation, we can add $2$ to both sides of choice (B) to see if we get the original equation. $12g − 2 + 2 = 7 + 2$ $12g = 9$ This is not equivalent to the original equation $12g = 8$ .
Check Choice (C): Analyze choice (C) $12g − 3 = 5$ . To check if this is equivalent to the original equation, we can add $3$ to both sides of choice (C) to see if we get the original equation. $12g − 3 + 3 = 5 + 3$ $12g = 8$ This is equivalent to the original equation $12g = 8$ .
Check Choice (D): Analyze choice (D) $12g − 4 = 2$ . To check if this is equivalent to the original equation, we can add $4$ to both sides of choice (D) to see if we get the original equation. $12g − 4 + 4 = 2 + 4$ $12g = 6$ This is not equivalent to the original equation $12g = 8$ .