Rania solves the equation below by first squaring both sides of the equation. -5=sqrt(3x-7) What extraneous solution does Rania obtain? x=

Square both sides: Square both sides of the equation to eliminate the square root. -5 = sqrt(3x - 7) (-5)^2 = (sqrt(3x - 7))^2 25 = 3x - 7Add 7 to isolate x: Add 7 to both sides of the equation to isolate the term with x. 25 + 7 = 3x - 7 + 7 32 = 3xDivide by 3 to solve for x: Divide both sides by 3 to solve for x. 32 / 3 = 3x / 3 x = 32 / 3Check the solution: Check the solution by substituting x back into the original equation. -5 = sqrt(3(32/3) - 7) -5 = sqrt(32 - 7) -5 = sqrt(25) -5 = 5 or -5 = -5 The original equation states -5 = sqrt(3x - 7), so the square root should only yield a positive result, meaning -5 = 5 is not possible. Therefore, x = 32/3 is an extraneous solution.

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Rania solves the equation below by first squaring both sides of the equation.

-5=sqrt(3x-7)
What extraneous solution does Rania obtain?

x=

Rania solves the equation below by first squaring both sides of the equation. $\newline$ $-5=\sqrt{3 x-7}$ $\newline$ What extraneous solution does Rania obtain? $\newline$ $x=$

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Q. Rania solves the equation below by first squaring both sides of the equation.

\newline

-5=\sqrt{3 x-7}

\newline

What extraneous solution does Rania obtain?

\newline

x=

Square both sides: Square both sides of the equation to eliminate the square root. $\newline$ $-5 = \sqrt{3x - 7}$ $\newline$ $(-5)^2 = (\sqrt{3x - 7})^2$ $\newline$ $25 = 3x - 7$
Add $7$ to isolate x: Add $7$ to both sides of the equation to isolate the term with x. $\newline$ $25 + 7 = 3x - 7 + 7$ $\newline$ $32 = 3x$
Divide by $3$ to solve for x: Divide both sides by $3$ to solve for x. $\newline$ $\frac{32}{3} = \frac{3x}{3}$ $\newline$ $x = \frac{32}{3}$
Check the solution: Check the solution by substituting $x$ back into the original equation. $\newline$ $-5 = \sqrt{3(\frac{32}{3}) - 7}$ $\newline$ $-5 = \sqrt{32 - 7}$ $\newline$ $-5 = \sqrt{25}$ $\newline$ $-5 = 5$ or $-5 = -5$ $\newline$ The original equation states $-5 = \sqrt{3x - 7}$ , so the square root should only yield a positive result, meaning $-5 = 5$ is not possible. Therefore, $x = \frac{32}{3}$ is an extraneous solution.