Select all of the equations below that are equivalent to: $\newline$ $w + -5 = 28$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $-3(w + -5) = -84$ $\newline$ (B) $-16w + 80 = -16 \cdot 28$ $\newline$ (C) $7w + -35 = 7 \cdot 28$ $\newline$ (D) $2(w + -5) = 56$

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Algebra 1

Identify equivalent equations

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

\newline

w + -5 = 28

\newline

Use properties of equality.

\newline

Multi-select Choices:

\newline

(A)

-3(w + -5) = -84

\newline

(B)

-16w + 80 = -16 \cdot 28

\newline

(C)

7w + -35 = 7 \cdot 28

\newline

(D)

2(w + -5) = 56

Identify Original Equation: First, let's identify the original equation we are comparing to: $\newline$ $w + (\text{-}5) = 28$ $\newline$ We need to determine which of the choices are equivalent to this equation by using properties of equality.
Check Option (A): Let's check option (A): $\newline$ (A) $-3(w + -5) = -84$ $\newline$ We can distribute the $-3$ to both $w$ and $-5$ : $\newline$ $-3w + 15 = -84$ $\newline$ This is not equivalent to the original equation because if we divide both sides by $-3$ to reverse the operation, we do not get the original equation.
Check Option (B): Let's check option (B): $\newline$ (B) $-16w + 80 = -16 \cdot 28$ $\newline$ First, calculate $-16 \cdot 28$ : $\newline$ $-16 \cdot 28 = -448$ $\newline$ Now the equation is: $\newline$ $-16w + 80 = -448$ $\newline$ This is not equivalent to the original equation because if we add $16w$ to both sides and then subtract $80$ from both sides, we do not get the original equation.
Check Option (C): Let's check option (C): $\newline$ (C) $7w + (-35) = 7 \cdot 28$ $\newline$ First, calculate $7 \cdot 28$ : $\newline$ $7 \cdot 28 = 196$ $\newline$ Now the equation is: $\newline$ $7w - 35 = 196$ $\newline$ This is equivalent to the original equation because if we divide both sides by $7$ to reverse the operation, we get the original equation: $\newline$ $w - 5 = 28$
Check Option (D): Let's check option (D): $\newline$ (D) $2(w + -5) = 56$ $\newline$ We can distribute the $2$ to both $w$ and $-5$ : $\newline$ $2w - 10 = 56$ $\newline$ This is equivalent to the original equation because if we divide both sides by $2$ to reverse the operation, we get the original equation: $\newline$ $w - 5 = 28$