Select all of the equations below that are equivalent to: $\newline$ $j + 5 = 3$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $22(j + 5) = 66$ $\newline$ (B) $(j + 5) \cdot 7 = 21$ $\newline$ (C) $-18(j + 5) = -36$ $\newline$ (D) $(j + 5) \cdot 23 = 69$

Full solution

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

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j + 5 = 3

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Use properties of equality.

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Multi-select Choices:

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(A)

22(j + 5) = 66

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(B)

(j + 5) \cdot 7 = 21

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(C)

-18(j + 5) = -36

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(D)

(j + 5) \cdot 23 = 69

Check Equation (A): To determine if the equations are equivalent, we need to see if they simplify to $j + 5 = 3$ when we apply the properties of equality.
Check Equation (B): Let's start with option (A) $22(j + 5) = 66$ . We divide both sides by $22$ to isolate $(j + 5)$ . $\frac{22(j + 5)}{22} = \frac{66}{22}$ $(j + 5) = 3$ This is equivalent to the original equation.
Check Equation (C): Now, let's check option (B) $(j + 5) \cdot 7 = 21$ . We divide both sides by $7$ to isolate $(j + 5)$ . $(j + 5) \cdot 7 / 7 = 21 / 7$ $(j + 5) = 3$ This is also equivalent to the original equation.
Check Equation (D): Next, we examine option (C) $-18(j + 5) = -36$ . $\newline$ We divide both sides by $-18$ to isolate $(j + 5)$ . $\newline$ $-18(j + 5) / -18 = -36 / -18$ $\newline$ $(j + 5) = 2$ $\newline$ This is not equivalent to the original equation.
Check Equation (D): Next, we examine option (C) $-18(j + 5) = -36$ . We divide both sides by $-18$ to isolate $(j + 5)$ . $-18(j + 5) / -18 = -36 / -18$ $(j + 5) = 2$ This is not equivalent to the original equation.Finally, we look at option (D) $(j + 5) \cdot 23 = 69$ . We divide both sides by $23$ to isolate $(j + 5)$ . $(j + 5) \cdot 23 / 23 = 69 / 23$ $(j + 5) = 3$ This is equivalent to the original equation.