Solve for x (7x)/9=7/x

$\frac{7 x}{9} = \frac{7}{x}$

Step 1

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$7 x \cdot x = 9 \cdot 7$

Step 2

Solve the equation for $x$ .

Simplify.

Raise $x$ to the power of $1$ .

$7 (x^{1} x) = 9 \cdot 7$

Raise $x$ to the power of $1$ .

$7 (x^{1} x^{1}) = 9 \cdot 7$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$7 x^{1 + 1} = 9 \cdot 7$

Add $1$ and $1$ .

$7 x^{2} = 9 \cdot 7$

Multiply $9$ by $7$ .

$7 x^{2} = 63$

Divide each term in $7 x^{2} = 63$ by $7$ and simplify.

Divide each term in $7 x^{2} = 63$ by $7$ .

$\frac{7 x^{2}}{7} = \frac{63}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x^{2}}{7} = \frac{63}{7}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{63}{7}$

Simplify the right side.

Divide $63$ by $7$ .

$x^{2} = 9$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 3$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 3$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 3$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 3$

Solve for x (7x)/9=7/x

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