Algebra Examples

$3 \sqrt[3]{x} = \sqrt[3]{7 x + 5}$

Step 1

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

${(3 \sqrt[3]{x})}^{3} = {\sqrt[3]{7 x + 5}}^{3}$

Step 2

Simplify each side of the equation.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x}$ as $x^{\frac{1}{3}}$ .

${(3 x^{\frac{1}{3}})}^{3} = {\sqrt[3]{7 x + 5}}^{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

Apply the product rule to $3 x^{\frac{1}{3}}$ .

$3^{3} {(x^{\frac{1}{3}})}^{3} = {\sqrt[3]{7 x + 5}}^{3}$

Step 2.2.1.2

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

$27 {(x^{\frac{1}{3}})}^{3} = {\sqrt[3]{7 x + 5}}^{3}$

Step 2.2.1.3

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

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Step 2.2.1.3.1

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

$27 x^{\frac{1}{3} \cdot 3} = {\sqrt[3]{7 x + 5}}^{3}$

Step 2.2.1.3.2

Cancel the common factor of $3$ .

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Step 2.2.1.3.2.1

Cancel the common factor.

$27 x^{\frac{1}{3} \cdot 3} = {\sqrt[3]{7 x + 5}}^{3}$

Step 2.2.1.3.2.2

Rewrite the expression.

$27 x^{1} = {\sqrt[3]{7 x + 5}}^{3}$

Step 2.2.1.4

Simplify.

$27 x = {\sqrt[3]{7 x + 5}}^{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Rewrite ${\sqrt[3]{7 x + 5}}^{3}$ as $7 x + 5$ .

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Step 2.3.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{7 x + 5}$ as ${(7 x + 5)}^{\frac{1}{3}}$ .

$27 x = {({(7 x + 5)}^{\frac{1}{3}})}^{3}$

Step 2.3.1.2

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

$27 x = {(7 x + 5)}^{\frac{1}{3} \cdot 3}$

Step 2.3.1.3

Combine $\frac{1}{3}$ and $3$ .

$27 x = {(7 x + 5)}^{\frac{3}{3}}$

Step 2.3.1.4

Cancel the common factor of $3$ .

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Step 2.3.1.4.1

Cancel the common factor.

$27 x = {(7 x + 5)}^{\frac{3}{3}}$

Step 2.3.1.4.2

Rewrite the expression.

$27 x = {(7 x + 5)}^{1}$

Step 2.3.1.5

Simplify.

$27 x = 7 x + 5$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Subtract $7 x$ from both sides of the equation.

$27 x - 7 x = 5$

Step 3.1.2

Subtract $7 x$ from $27 x$ .

$20 x = 5$

Step 3.2

Divide each term in $20 x = 5$ by $20$ and simplify.

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Step 3.2.1

Divide each term in $20 x = 5$ by $20$ .

$\frac{20 x}{20} = \frac{5}{20}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $20$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{20 x}{20} = \frac{5}{20}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{20}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Cancel the common factor of $5$ and $20$ .

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Step 3.2.3.1.1

Factor $5$ out of $5$ .

$x = \frac{5 (1)}{20}$

Step 3.2.3.1.2

Cancel the common factors.

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Step 3.2.3.1.2.1

Factor $5$ out of $20$ .

$x = \frac{5 \cdot 1}{5 \cdot 4}$

Step 3.2.3.1.2.2

Cancel the common factor.

$x = \frac{5 \cdot 1}{5 \cdot 4}$

Step 3.2.3.1.2.3

Rewrite the expression.

$x = \frac{1}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{4}$

Decimal Form:

$x = 0.25$