Algebra Examples

$\sqrt[3]{5 x + 10} - \sqrt[3]{x - 4} = 0$

Step 1

Add $\sqrt[3]{x - 4}$ to both sides of the equation.

$\sqrt[3]{5 x + 10} = \sqrt[3]{x - 4}$

Step 2

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

${\sqrt[3]{5 x + 10}}^{3} = {\sqrt[3]{x - 4}}^{3}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5 x + 10}$ as ${(5 x + 10)}^{\frac{1}{3}}$ .

${({(5 x + 10)}^{\frac{1}{3}})}^{3} = {\sqrt[3]{x - 4}}^{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(5 x + 10)}^{\frac{1}{3}})}^{3}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(5 x + 10)}^{\frac{1}{3}})}^{3}$ .

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Step 3.2.1.1.1

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

${(5 x + 10)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{x - 4}}^{3}$

Step 3.2.1.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(5 x + 10)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{x - 4}}^{3}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(5 x + 10)}^{1} = {\sqrt[3]{x - 4}}^{3}$

Step 3.2.1.2

Simplify.

$5 x + 10 = {\sqrt[3]{x - 4}}^{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Rewrite ${\sqrt[3]{x - 4}}^{3}$ as $x - 4$ .

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Step 3.3.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x - 4}$ as ${(x - 4)}^{\frac{1}{3}}$ .

$5 x + 10 = {({(x - 4)}^{\frac{1}{3}})}^{3}$

Step 3.3.1.2

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

$5 x + 10 = {(x - 4)}^{\frac{1}{3} \cdot 3}$

Step 3.3.1.3

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

$5 x + 10 = {(x - 4)}^{\frac{3}{3}}$

Step 3.3.1.4

Cancel the common factor of $3$ .

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Step 3.3.1.4.1

Cancel the common factor.

$5 x + 10 = {(x - 4)}^{\frac{3}{3}}$

Step 3.3.1.4.2

Rewrite the expression.

$5 x + 10 = {(x - 4)}^{1}$

Step 3.3.1.5

Simplify.

$5 x + 10 = x - 4$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $x$ from both sides of the equation.

$5 x + 10 - x = - 4$

Step 4.1.2

Subtract $x$ from $5 x$ .

$4 x + 10 = - 4$

Step 4.2

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

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Step 4.2.1

Subtract $10$ from both sides of the equation.

$4 x = - 4 - 10$

Step 4.2.2

Subtract $10$ from $- 4$ .

$4 x = - 14$

Step 4.3

Divide each term in $4 x = - 14$ by $4$ and simplify.

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Step 4.3.1

Divide each term in $4 x = - 14$ by $4$ .

$\frac{4 x}{4} = \frac{- 14}{4}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $4$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 14}{4}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 14}{4}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of $- 14$ and $4$ .

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Step 4.3.3.1.1

Factor $2$ out of $- 14$ .

$x = \frac{2 (- 7)}{4}$

Step 4.3.3.1.2

Cancel the common factors.

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Step 4.3.3.1.2.1

Factor $2$ out of $4$ .

$x = \frac{2 \cdot - 7}{2 \cdot 2}$

Step 4.3.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot - 7}{2 \cdot 2}$

Step 4.3.3.1.2.3

Rewrite the expression.

$x = \frac{- 7}{2}$

Step 4.3.3.2

Move the negative in front of the fraction.

$x = - \frac{7}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7}{2}$

Decimal Form:

$x = - 3.5$

Mixed Number Form:

$x = - 3 \frac{1}{2}$