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Which equation has both $3$ and $-3$ as possible values of $x$ ? Select all that apply. $\newline$ Multi-select Choices: $\newline$ (A) $x^2 = 6$ $\newline$ (B) $x^3 = 6$ $\newline$ (C) $x^2 = 9$ $\newline$ (D) $x^3 = 9$ $\newline$ (E) $x^2 = 27$ $\newline$ (F) $x^3 = 27$

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Simplify rational expressions

Full solution

Q. Which equation has both

3

and

-3

as possible values of

x

? Select all that apply.

\newline

Multi-select Choices:

\newline

(A)

x^2 = 6

\newline

(B)

x^3 = 6

\newline

(C)

x^2 = 9

\newline

(D)

x^3 = 9

\newline

(E)

x^2 = 27

\newline

(F)

x^3 = 27

Check Equation (A): Step $1$ : Check equation (A) $x^2 = 6$ . $\newline$ Plug in $x = 3$ and $x = -3$ : $\newline$ $3^2 = 9$ and $(-3)^2 = 9$ . $\newline$ Both are not equal to $6$ .
Check Equation (B): Step $2$ : Check equation (B) $x^3 = 6$ . $\newline$ Plug in $x = 3$ and $x = -3$ : $\newline$ $3^3 = 27$ and $(-3)^3 = -27$ . $\newline$ Neither equals $6$ .
Check Equation (C): Step $3$ : Check equation (C) $x^2 = 9$ . $\newline$ Plug in $x = 3$ and $x = -3$ : $\newline$ $3^2 = 9$ and $(-3)^2 = 9$ . $\newline$ Both equal $9$ , so this equation works.
Check Equation (D): Step $4$ : Check equation (D) $x^3 = 9$ . $\newline$ Plug in $x = 3$ and $x = -3$ : $\newline$ $3^3 = 27$ and $(-3)^3 = -27$ . $\newline$ Neither equals $9$ .
Check Equation (E): Step $5$ : Check equation (E) $x^2 = 27$ . $\newline$ Plug in $x = 3$ and $x = -3$ : $\newline$ $3^2 = 9$ and $(-3)^2 = 9$ . $\newline$ Both are not equal to $27$ .
Check Equation (F): Step $6$ : Check equation (F) $x^3 = 27$ . $\newline$ Plug in $x = 3$ and $x = -3$ : $\newline$ $3^3 = 27$ and $(-3)^3 = -27$ . $\newline$ Only $x = 3$ equals $27$ , not $-3$ .

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