Algebra Examples

$\frac{3}{2} \sqrt[3]{5 x + 9} = 6$

Step 1

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

$\frac{2}{3} (\frac{3}{2} \cdot \sqrt[3]{5 x + 9}) = \frac{2}{3} \cdot 6$

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 $\frac{2}{3} (\frac{3}{2} \cdot \sqrt[3]{5 x + 9})$ .

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Step 2.1.1.1

Combine $\frac{3}{2}$ and $\sqrt[3]{5 x + 9}$ .

$\frac{2}{3} \cdot \frac{3 \sqrt[3]{5 x + 9}}{2} = \frac{2}{3} \cdot 6$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 \sqrt[3]{5 x + 9}}{2} = \frac{2}{3} \cdot 6$

Step 2.1.1.2.2

Rewrite the expression.

$\frac{1}{3} (3 \sqrt[3]{5 x + 9}) = \frac{2}{3} \cdot 6$

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Factor $3$ out of $3 \sqrt[3]{5 x + 9}$ .

$\frac{1}{3} (3 (\sqrt[3]{5 x + 9})) = \frac{2}{3} \cdot 6$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{1}{3} (3 \sqrt[3]{5 x + 9}) = \frac{2}{3} \cdot 6$

Step 2.1.1.3.3

Rewrite the expression.

$\sqrt[3]{5 x + 9} = \frac{2}{3} \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

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

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Factor $3$ out of $6$ .

$\sqrt[3]{5 x + 9} = \frac{2}{3} \cdot (3 (2))$

Step 2.2.1.1.2

Cancel the common factor.

$\sqrt[3]{5 x + 9} = \frac{2}{3} \cdot (3 \cdot 2)$

Step 2.2.1.1.3

Rewrite the expression.

$\sqrt[3]{5 x + 9} = 2 \cdot 2$

Step 2.2.1.2

Multiply $2$ by $2$ .

$\sqrt[3]{5 x + 9} = 4$

Step 3

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

${\sqrt[3]{5 x + 9}}^{3} = 4^{3}$

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 $\sqrt[3]{5 x + 9}$ as ${(5 x + 9)}^{\frac{1}{3}}$ .

${({(5 x + 9)}^{\frac{1}{3}})}^{3} = 4^{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify ${({(5 x + 9)}^{\frac{1}{3}})}^{3}$ .

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Step 4.2.1.1

Multiply the exponents in ${({(5 x + 9)}^{\frac{1}{3}})}^{3}$ .

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Step 4.2.1.1.1

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

${(5 x + 9)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Step 4.2.1.1.2

Cancel the common factor of $3$ .

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Step 4.2.1.1.2.1

Cancel the common factor.

${(5 x + 9)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Step 4.2.1.1.2.2

Rewrite the expression.

${(5 x + 9)}^{1} = 4^{3}$

Step 4.2.1.2

Simplify.

$5 x + 9 = 4^{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Raise $4$ to the power of $3$ .

$5 x + 9 = 64$

Step 5

Solve for $x$ .

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Step 5.1

Move all terms not containing $x$ to the right side of the equation.

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Step 5.1.1

Subtract $9$ from both sides of the equation.

$5 x = 64 - 9$

Step 5.1.2

Subtract $9$ from $64$ .

$5 x = 55$

Step 5.2

Divide each term in $5 x = 55$ by $5$ and simplify.

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Step 5.2.1

Divide each term in $5 x = 55$ by $5$ .

$\frac{5 x}{5} = \frac{55}{5}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $5$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{55}{5}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{55}{5}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $55$ by $5$ .

$x = 11$