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

Question

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

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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 ≠ 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 ≠ 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 ≠ s + 6, choice (D) is not equivalent to the original equation.

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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