Select all of the equations below that are equivalent to: $\newline$ $-21 = 4r$ $\newline$ Use properties of equality. $\newline$ $\newline$ Multi-select Choices: $\newline$ (A) $-22 \cdot -21 = -88r$ $\newline$ (B) $-23 \cdot -21 = -92r$ $\newline$ (C) $42 = 4r \cdot -2$ $\newline$ (D) $-84 = 4r \cdot 4$

View step-by-step help

Home

Math Problems

Algebra 1

Identify equivalent equations

Full solution

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

\newline

-21 = 4r

\newline

Use properties of equality.

\newline

\newline

Multi-select Choices:

\newline

(A)

-22 \cdot -21 = -88r

\newline

(B)

-23 \cdot -21 = -92r

\newline

(C)

42 = 4r \cdot -2

\newline

(D)

-84 = 4r \cdot 4

Check Equivalence Operation: Which operation should be used to check if the equations are equivalent? $\newline$ To check if the equations are equivalent, we need to see if the operations performed on both sides of the original equation maintain equality.
Check Equation (A): Check equation (A) $-22 \cdot -21 = -88r$ . To see if this equation is equivalent to $-21 = 4r$ , we need to simplify the left side and see if the right side has been multiplied by the same factor. $-22 \cdot -21 = 462$ (since multiplying two negatives gives a positive) This does not match the original equation because the left side of the original equation is $-21$ , not $462$ .
Check Equation (B): Check equation (B) $–23 \cdot –21 = –92r$ . To see if this equation is equivalent to $–21 = 4r$ , we need to simplify the left side and see if the right side has been multiplied by the same factor. $–23 \cdot –21 = 483$ (since multiplying two negatives gives a positive) This does not match the original equation because the left side of the original equation is $–21$ , not $483$ .
Check Equation (C): Check equation (C) $42 = 4r \cdot -2$ . To see if this equation is equivalent to $-21 = 4r$ , we need to simplify the right side and see if it matches the left side when the same operation is applied. $4r \cdot -2 = -8r$ This does not match the original equation because the right side of the original equation is $4r$ , not $-8r$ .
Check Equation (D): Check equation (D) $–84 = 4r \cdot 4$ . To see if this equation is equivalent to $–21 = 4r$ , we need to simplify the right side and see if it matches the left side when the same operation is applied. $4r \cdot 4 = 16r$ This does not match the original equation because the right side of the original equation is $4r$ , not $16r$ .