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

Solve for all values of x x .\newlinex9=9x \frac{x}{9}=\frac{9}{x} \newlineAnswer: x= x=

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Full solution

Q. Solve for all values of x x .\newlinex9=9x \frac{x}{9}=\frac{9}{x} \newlineAnswer: x= x=
  1. Cross-Multiply: Cross-multiply to eliminate the fractions.\newlineTo solve the equation (x9=9x)(\frac{x}{9}=\frac{9}{x}), we can cross-multiply to get rid of the fractions. This means we will multiply xx by xx and 99 by 99.\newlineCalculation: x×x=9×9x \times x = 9 \times 9
  2. Simplify Equation: Simplify the equation.\newlineAfter cross-multiplying, we get x2=81x^2 = 81.
  3. Find Square Root: Find the square root of both sides of the equation.\newlineTo solve for xx, we take the square root of both sides of the equation. Remember that taking the square root of a number gives us two possible values: one positive and one negative.\newlineCalculation: x=±81x = \pm\sqrt{81}
  4. Simplify Square Root: Simplify the square root.\newlineThe square root of 8181 is 99. Therefore, we have two possible solutions for xx.\newlineCalculation: x=±9x = \pm9

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