Select all of the equations below that are equivalent to: $\newline$ $54 = st$ $\newline$ Use properties of equality. $\newline$ $\newline$ Multi-select Choices: $\newline$ (A) $27 = \frac{st}{2}$ $\newline$ (B) $3 = \frac{st}{18}$ $\newline$ (C) $8 = \frac{st}{6}$ $\newline$ (D) $\text{–}27 = \frac{st}{\text{–}2}$

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Math Problems

Algebra 1

Identify equivalent equations

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

\newline

54 = st

\newline

Use properties of equality.

\newline

\newline

Multi-select Choices:

\newline

(A)

27 = \frac{st}{2}

\newline

(B)

3 = \frac{st}{18}

\newline

(C)

8 = \frac{st}{6}

\newline

(D)

\text{–}27 = \frac{st}{\text{–}2}

Given Equation Manipulation: We are given the equation $54 = st$ . To find equivalent equations, we can manipulate this equation using properties of equality, such as multiplication or division by the same non-zero number on both sides of the equation. Let's start by checking option (A).
Check Option (A): For option (A), $27 = \frac{st}{2}$ , we need to check if multiplying both sides by $2$ gives us the original equation. Let's do the calculation: $\newline$ $27 \times 2 = \frac{st}{2} \times 2$ $\newline$ $54 = st$ $\newline$ This is the same as the original equation, so (A) is equivalent.
Check Option (B): Now let's check option (B), $3 = \frac{st}{18}$ . We need to check if multiplying both sides by $18$ gives us the original equation. Let's do the calculation: $\newline$ $3 \times 18 = \frac{st}{18} \times 18$ $\newline$ $54 = st$ $\newline$ This is also the same as the original equation, so (B) is equivalent.
Check Option (C): Next, let's check option (C), $8 = \frac{st}{6}$ . We need to check if multiplying both sides by $6$ gives us the original equation. Let's do the calculation: $\newline$ $8 \times 6 = \frac{st}{6} \times 6$ $\newline$ $48 = st$ $\newline$ This is not the same as the original equation, so (C) is not equivalent.
Check Option (D): Finally, let's check option (D), $-27 = \frac{st}{-2}$ . We need to check if multiplying both sides by $-2$ gives us the original equation. Let's do the calculation: $\newline$ $-27 \times -2 = \frac{st}{-2} \times -2$ $\newline$ $54 = st$ $\newline$ This is the same as the original equation, so (D) is equivalent.