Algebra Examples

$\frac{2}{3} \sqrt{x} = 6$

Step 1

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} (\frac{2}{3} \cdot \sqrt{x}) = \frac{3}{2} \cdot 6$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{3}{2} (\frac{2}{3} \cdot \sqrt{x})$ .

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Step 2.1.1.1

Combine $\frac{2}{3}$ and $\sqrt{x}$ .

$\frac{3}{2} \cdot \frac{2 \sqrt{x}}{3} = \frac{3}{2} \cdot 6$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 \sqrt{x}}{3} = \frac{3}{2} \cdot 6$

Step 2.1.1.2.2

Rewrite the expression.

$\frac{1}{2} (2 \sqrt{x}) = \frac{3}{2} \cdot 6$

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

Factor $2$ out of $2 \sqrt{x}$ .

$\frac{1}{2} (2 (\sqrt{x})) = \frac{3}{2} \cdot 6$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{1}{2} (2 \sqrt{x}) = \frac{3}{2} \cdot 6$

Step 2.1.1.3.3

Rewrite the expression.

$\sqrt{x} = \frac{3}{2} \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{3}{2} \cdot 6$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Factor $2$ out of $6$ .

$\sqrt{x} = \frac{3}{2} \cdot (2 (3))$

Step 2.2.1.1.2

Cancel the common factor.

$\sqrt{x} = \frac{3}{2} \cdot (2 \cdot 3)$

Step 2.2.1.1.3

Rewrite the expression.

$\sqrt{x} = 3 \cdot 3$

Step 2.2.1.2

Multiply $3$ by $3$ .

$\sqrt{x} = 9$

Step 3

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{x}}^{2} = 9^{2}$

Step 4

Simplify each side of the equation.

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(x^{\frac{1}{2}})}^{2} = 9^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify ${(x^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.1

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} = 9^{2}$

Step 4.2.1.1.2

Cancel the common factor of $2$ .

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Step 4.2.1.1.2.1

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 9^{2}$

Step 4.2.1.1.2.2

Rewrite the expression.

$x^{1} = 9^{2}$

Step 4.2.1.2

Simplify.

$x = 9^{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Raise $9$ to the power of $2$ .

$x = 81$