Select all of the equations below that are equivalent to: $\newline$ $p + q = 33$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $(p + q) \cdot -3 = -99$ $\newline$ (B) $(p + q) \cdot 2 = 66$ $\newline$ (C) $3(p + q) = 99$ $\newline$ (D) $(p + q) \cdot -2 = -66$

Full solution

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

\newline

p + q = 33

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Use properties of equality.

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Multi-select Choices:

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(A)

(p + q) \cdot -3 = -99

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(B)

(p + q) \cdot 2 = 66

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(C)

3(p + q) = 99

\newline

(D)

(p + q) \cdot -2 = -66

Identify equation and property: Step $1$ : Identify the given equation and the property to use. $\newline$ We know $p + q = 33$ . We need to check which options are equivalent using multiplication or division properties of equality.
Check option (A): Step $2$ : Check option (A) $(p + q) \cdot -3 = -99$ . $\newline$ Multiply the left side of the given equation by $-3$ : $(p + q) \cdot -3 = 33 \cdot -3 = -99$ .
Check option (B): Step $3$ : Check option (B) $(p + q) \cdot 2 = 66$ . $\newline$ Multiply the left side of the given equation by $2$ : $(p + q) \cdot 2 = 33 \cdot 2 = 66$ .
Check option (C): Step $4$ : Check option (C) $3(p + q) = 99$ . Multiply the left side of the given equation by $3$ : $3 \times (p + q) = 3 \times 33 = 99$ .
Check option (D): Step $5$ : Check option (D) $(p + q) \cdot -2 = -66$ . $\newline$ Multiply the left side of the given equation by $-2$ : $(p + q) \cdot -2 = 33 \cdot -2 = -66$ .