Select all of the equations below that are equivalent to: $\newline$ $20 = y - z$ $\newline$ Use properties of equality. $\newline$ $\newline$ Multi-select Choices: $\newline$ (A) $16 = y - z - 4$ $\newline$ (B) $7 = y - z - 13$ $\newline$ (C) $18 = y - z - 2$ $\newline$ (D) $8 = y - z - 12$

Full solution

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

\newline

20 = y - z

\newline

Use properties of equality.

\newline

\newline

Multi-select Choices:

\newline

(A)

16 = y - z - 4

\newline

(B)

7 = y - z - 13

\newline

(C)

18 = y - z - 2

\newline

(D)

8 = y - z - 12

Manipulate Original Equation: To determine if an equation is equivalent to $20 = y - z$ , we can manipulate the original equation using properties of equality and compare it to each choice.
Check Choice (A): Let's start with choice (A) $16 = y - z - 4$ . To check if it's equivalent, we can add $4$ to both sides of the original equation. $\newline$ $20 + 4 = y - z + 4$ $\newline$ $24 = y - z$ $\newline$ This is not equivalent to $16 = y - z - 4$ .
Check Choice (B): Now let's check choice (B) $7 = y - z - 13$ . We add $13$ to both sides of the original equation. $\newline$ $20 + 13 = y - z + 13$ $\newline$ $33 = y - z$ $\newline$ This is not equivalent to $7 = y - z - 13$ .
Check Choice (C): Next, we examine choice (C) $18 = y - z - 2$ . We add $2$ to both sides of the original equation. $\newline$ $20 + 2 = y - z + 2$ $\newline$ $22 = y - z$ $\newline$ This is not equivalent to $18 = y - z - 2$ .
Check Choice (D): Finally, we look at choice (D) $8 = y - z - 12$ . We add $12$ to both sides of the original equation. $\newline$ $20 + 12 = y - z + 12$ $\newline$ $32 = y - z$ $\newline$ This is not equivalent to $8 = y - z - 12$ .