Select all of the equations below that are equivalent to: $\newline$ $9 = s + 9$ $\newline$ Use properties of equality. $\newline$ $\newline$ Multi-select Choices: $\newline$ (A) $9 + 3 = s + 12$ $\newline$ (B) $9 + 6 = s + 13$ $\newline$ (C) $19 = 11 + s + 9$ $\newline$ (D) $9 + 8 = s + 15$

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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

9 = s + 9

\newline

Use properties of equality.

\newline

\newline

Multi-select Choices:

\newline

(A)

9 + 3 = s + 12

\newline

(B)

9 + 6 = s + 13

\newline

(C)

19 = 11 + s + 9

\newline

(D)

9 + 8 = s + 15

Original Equation Analysis: We start with the original equation: $9 = s + 9$ . To determine if other equations are equivalent, we can simplify or manipulate the original equation using properties of equality without changing its meaning.
Choice (A) Evaluation: Let's analyze choice (A) $9 + 3 = s + 12$ . We can simplify both sides of the original equation by subtracting $9$ from each side to isolate $s$ : $9 - 9 = s + 9 - 9$ , which simplifies to $0 = s$ . Now, let's apply the same operation to choice (A): $9 + 3 - 9 = s + 12 - 9$ , which simplifies to $3 = s + 3$ . Since $0 = s$ , adding $3$ to both sides should give us $3 = s + 3$ , which is what we have here. So, choice (A) is equivalent to the original equation.
Choice (B) Evaluation: Next, let's look at choice (B) $9 + 6 = s + 13$ . Using the simplified form of the original equation, $0 = s$ , we add $6$ to both sides: $0 + 6 = s + 6$ , which gives us $6 = s + 6$ . Now, let's apply the same operation to choice (B): $9 + 6 - 9 = s + 13 - 9$ , which simplifies to $6 = s + 4$ . Since $6 \neq s + 4$ , choice (B) is not equivalent to the original equation.
Choice (C) Evaluation: Now, let's examine choice (C) $19 = 11 + s + 9$ . We can simplify the right side by combining like terms: $11 + s + 9 = s + 20$ . Now, let's compare it to the simplified original equation, $0 = s$ . If we add $20$ to both sides of the original equation, we get $20 = s + 20$ . Since $19 \neq 20$ , choice (C) is not equivalent to the original equation.
Choice (D) Evaluation: Finally, let's consider choice (D) $9 + 8 = s + 15$ . Using the simplified form of the original equation, $0 = s$ , we add $8$ to both sides: $0 + 8 = s + 8$ , which gives us $8 = s + 8$ . Now, let's apply the same operation to choice (D): $9 + 8 - 9 = s + 15 - 9$ , which simplifies to $8 = s + 6$ . Since $8 \neq s + 6$ , choice (D) is not equivalent to the original equation.