Select all of the equations below that are equivalent to: $\newline$ $9 = n + -3$ $\newline$ Use properties of equality. $\newline$ Multi-select Choices: $\newline$ (A) $64 = (n + -3) \cdot 8$ $\newline$ (B) $-77 = -7(n + -3)$ $\newline$ (C) $90 = (n + -3) \cdot 10$ $\newline$ (D) $63 = (n + -3) \cdot 7$

View step-by-step help

Home

Math Problems

Algebra 2

Quadratic equation with complex roots

Full solution

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

\newline

9 = n + -3

\newline

Use properties of equality.

\newline

Multi-select Choices:

\newline

(A)

64 = (n + -3) \cdot 8

\newline

(B)

-77 = -7(n + -3)

\newline

(C)

90 = (n + -3) \cdot 10

\newline

(D)

63 = (n + -3) \cdot 7

Understand Equation: Understand the original equation. $\newline$ The original equation is $9 = n + (-3)$ . To find equivalent equations, we can perform the same operation on both sides of the equation without changing its meaning.
Check Equation (A): Check equation (A) $64 = (n + (\text{–}3)) \cdot 8$ . Multiply the right side of the original equation by $8$ : $(n + (\text{–}3)) \cdot 8 = 9 \cdot 8$ . Calculate $9 \cdot 8 = 72$ . Check if $72$ equals $64$ .
Equation (A) Comparison: Since $72$ does not equal $64$ , equation (A) is not equivalent to the original equation.
Check Equation (B): Check equation (B) $-77 = -7(n + (-3))$ . Multiply the right side of the original equation by $-7$ : $-7(n + (-3)) = 9 \cdot (-7)$ . Calculate $9 \cdot (-7) = -63$ . Check if $-63$ equals $-77$ .
Equation (B) Comparison: Since $-63$ does not equal $-77$ , equation (B) is not equivalent to the original equation.
Check Equation (C): Check equation (C) $90 = (n + (–3)) \cdot 10$ . Multiply the right side of the original equation by $10$ : $(n + (–3)) \cdot 10 = 9 \cdot 10$ . Calculate $9 \cdot 10 = 90$ . Check if $90$ equals $90$ .
Equation (C) Comparison: Since $90$ equals $90$ , equation (C) is equivalent to the original equation.
Check Equation (D): Check equation (D) $63 = (n + (–3)) \cdot 7$ . Multiply the right side of the original equation by $7$ : $(n + (–3)) \cdot 7 = 9 \cdot 7$ . Calculate $9 \cdot 7 = 63$ . Check if $63$ equals $63$ .
Equation (D) Comparison: Since $63$ equals $63$ , equation (D) is equivalent to the original equation.