Select all of the equations below that are equivalent to: b + c = –25 Use properties of equality. Multi-select Choices: (A)–4(b + c) = 100 (B)(b + c) · –2 = 50 (C)(b + c) · –3 = 75 (D)3(b + c) = –75

Given Equation: We are given the equation b + c = –25. We need to determine which of the multiple-choice options are equivalent to this equation by using properties of equality.Check Option (A): Let's start with option (A): –4(b + c) = 100. To check if this is equivalent, we can divide both sides of the equation by –4 to see if we get the original equation. –4(b + c) / –4 = 100 / –4 b + c = –25 This is equivalent to the original equation.Check Option (B): Now, let's check option (B): (b + c) · –2 = 50. We can divide both sides by –2 to see if it simplifies to the original equation. (b + c) · –2 / –2 = 50 / –2 b + c = –25 This is also equivalent to the original equation.Check Option (C: Next, we check option (C): (b + c) · –3 = 75. We divide both sides by –3 to check for equivalence. (b + c) · –3 / –3 = 75 / –3 b + c = –25 This is not equivalent to the original equation because the correct division should give us b + c = –25.

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Select all of the equations below that are equivalent to: $\newline$ $b + c = -25$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $-4(b + c) = 100$ $\newline$ (B) $(b + c) \cdot -2 = 50$ $\newline$ (C) $(b + c) \cdot -3 = 75$ $\newline$ (D) $3(b + c) = -75$

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Math Problems

Algebra 1

Identify equivalent equations

Full solution

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

\newline

b + c = -25

\newline

Use properties of equality.

\newline

Multi-select Choices:

\newline

(A)

-4(b + c) = 100

\newline

(B)

(b + c) \cdot -2 = 50

\newline

(C)

(b + c) \cdot -3 = 75

\newline

(D)

3(b + c) = -75

Given Equation: We are given the equation $b + c = -25$ . We need to determine which of the multiple-choice options are equivalent to this equation by using properties of equality.
Check Option (A): Let's start with option (A): $-4(b + c) = 100$ . To check if this is equivalent, we can divide both sides of the equation by $-4$ to see if we get the original equation. $\newline$ $-4(b + c) / -4 = 100 / -4$ $\newline$ $b + c = -25$ $\newline$ This is equivalent to the original equation.
Check Option (B): Now, let's check option (B): b + c) \cdot (–2) = 50\. We can divide both sides by \$–2 to see if it simplifies to the original equation.(\newline\)(b + c) \cdot (–$2) / (– $2$ ) = $50$ / (– $2$ )(\newline$\b + c = – $25$ (\newline\)This is also equivalent to the original equation.
Check Option (C: Next, we check option (C): b + c) \cdot (–3) = 75\. We divide both sides by \$–3 to check for equivalence.(\newline\) $(b + c) \cdot (–3) / (–3) = 75 / (–3)(\newline$ \$b + c = –25(\newline\)This is not equivalent to the original equation because the correct division should give us \$b + c = –25\).