Solve for all values of x. (9)/(x)=(x)/(9) Answer: x=

Cross-Multiply to Eliminate Fractions: Cross-multiply to eliminate the fractions. 9 * 9 = x * x This gives us 81 = x^2.Solve the Quadratic Equation: Solve the quadratic equation. To find the values of x, we take the square root of both sides of the equation. √81 = √x^2 This gives us x = ±9, since both 9 and -9 squared will give us 81.Check for Extraneous Solutions: Check for extraneous solutions. We substitute x = 9 and x = -9 back into the original equation to ensure they are valid solutions. For x = 9: (9)/(9) = (9)/(9) which simplifies to 1 = 1, which is true. For x = -9: (9)/(-9) = (-9)/(9) which simplifies to -1 = -1, which is also true. Therefore, both solutions are valid.

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Solve for all values of
x.

(9)/(x)=(x)/(9)
Answer:
x=

Solve for all values of $x$ . $\newline$ $\frac{9}{x}=\frac{x}{9}$ $\newline$ Answer: $x=$

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Math Problems

Grade 7

Powers with negative bases

Full solution

Q. Solve for all values of

x

\newline

\frac{9}{x}=\frac{x}{9}

\newline

Answer:

x=

Cross-Multiply to Eliminate Fractions: Cross-multiply to eliminate the fractions. $\newline$ $9 \times 9 = x \times x$ $\newline$ This gives us $81 = x^2$ .
Solve the Quadratic Equation: Solve the quadratic equation. $\newline$ To find the values of $x$ , we take the square root of both sides of the equation. $\newline$ $\sqrt{81} = \sqrt{x^2}$ $\newline$ This gives us $x = \pm9$ , since both $9$ and $-9$ squared will give us $81$ .
Check for Extraneous Solutions: Check for extraneous solutions. We substitute $x = 9$ and $x = -9$ back into the original equation to ensure they are valid solutions. For $x = 9$ : $\frac{9}{9} = \frac{9}{9}$ which simplifies to $1 = 1$ , which is true. For $x = -9$ : $\frac{9}{-9} = \frac{-9}{9}$ which simplifies to $-1 = -1$ , which is also true. Therefore, both solutions are valid.