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Select all of the equations below that are equivalent to: $\newline$ $13q = 16$ $\newline$ Use properties of equality. $\newline$ $\newline$ Multi-select Choices: $\newline$ (A) $13q − 10 = 6$ $\newline$ (B) $13q − 3 = 11$ $\newline$ (C) $13q − 8 = 8$ $\newline$ (D) $13q − 5 = 9$

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Identify equivalent equations

Full solution

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

\newline

13q = 16

\newline

Use properties of equality.

\newline

\newline

Multi-select Choices:

\newline

(A)

13q  −  10 = 6

\newline

(B)

13q  −  3 = 11

\newline

(C)

13q  −  8 = 8

\newline

(D)

13q  −  5 = 9

Analyze Equation: Step $1$ : Analyze the original equation $13q = 16$ to understand what transformations are needed to check equivalency.
Transform Equation (A): Step $2$ : Transform the equation (A) $13q - 10 = 6$ to check if it's equivalent to $13q = 16$ . Add $10$ to both sides: $13q - 10 + 10 = 6 + 10$ which simplifies to $13q = 16$ .
Transform Equation (B): Step $3$ : Transform the equation (B) $13q - 3 = 11$ to check if it's equivalent to $13q = 16$ . Add $3$ to both sides: $13q - 3 + 3 = 11 + 3$ which simplifies to $13q = 14$ .
Transform Equation (C): Step $4$ : Transform the equation (C) $13q - 8 = 8$ to check if it's equivalent to $13q = 16$ . $\newline$ Add $8$ to both sides: $13q - 8 + 8 = 8 + 8$ which simplifies to $13q = 16$ .
Transform Equation (D): Step $5$ : Transform the equation (D) $13q - 5 = 9$ to check if it's equivalent to $13q = 16$ . Add $5$ to both sides: $13q - 5 + 5 = 9 + 5$ which simplifies to $13q = 14$ .

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