Select all of the equations below that are equivalent to: q + –5 = –21 Use properties of equality. Multi-select Choices: (A)–15q + 75 = –15 · –21 (B)–5q + 25 = –5 · –21 (C)–2q + 10 = –2 · –21 (D)(q + –5) · –4 = 84

Given Equation Analysis: We are given the equation q + –5 = –21. To determine if the other equations are equivalent, we need to apply properties of equality to transform the given equation and compare it with each choice.Choice (A) Evaluation: Let's start with choice (A): –15q + 75 = –15 · –21. We can apply the distributive property to the right side of the equation to see if it simplifies to q + –5 = –21. Distribute –15 to –21: –15 * –21 = 315. Now the equation is –15q + 75 = 315. To check if it's equivalent, we need to divide all terms by –15 to see if we get q + –5 = –21. Divide by –15: q = –5, which is not the same as q + –5 = –21.

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Select all of the equations below that are equivalent to: $\newline$ $q + -5 = -21$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $-15q + 75 = -15 \cdot -21$ $\newline$ (B) $-5q + 25 = -5 \cdot -21$ $\newline$ (C) $-2q + 10 = -2 \cdot -21$ $\newline$ (D) $(q + -5) \cdot -4 = 84$

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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

q + -5 = -21

\newline

Use properties of equality.

\newline

Multi-select Choices:

\newline

(A)

-15q + 75 = -15 \cdot -21

\newline

(B)

-5q + 25 = -5 \cdot -21

\newline

(C)

-2q + 10 = -2 \cdot -21

\newline

(D)

(q + -5) \cdot -4 = 84

Given Equation Analysis: We are given the equation $q + (-5) = -21$ . To determine if the other equations are equivalent, we need to apply properties of equality to transform the given equation and compare it with each choice.
Choice (A) Evaluation: Let's start with choice (A): $-15q + 75 = -15 \cdot -21$ . We can apply the distributive property to the right side of the equation to see if it simplifies to $q + -5 = -21$ . $\newline$ Distribute $-15$ to $-21$ : $-15 \times -21 = 315$ . $\newline$ Now the equation is $-15q + 75 = 315$ . To check if it's equivalent, we need to divide all terms by $-15$ to see if we get $q + -5 = -21$ . $\newline$ Divide by $-15$ : $q = -5$ , which is not the same as $q + -5 = -21$ .