Algebra Examples

$y = 2 \sqrt[3]{x + 2} - 4$

Step 1

Set $2 \sqrt[3]{x + 2} - 4$ equal to $0$ .

$2 \sqrt[3]{x + 2} - 4 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $4$ to both sides of the equation.

$2 \sqrt[3]{x + 2} = 4$

Step 2.2

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

${(2 \sqrt[3]{x + 2})}^{3} = 4^{3}$

Step 2.3

Simplify each side of the equation.

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Step 2.3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x + 2}$ as ${(x + 2)}^{\frac{1}{3}}$ .

${(2 {(x + 2)}^{\frac{1}{3}})}^{3} = 4^{3}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Simplify ${(2 {(x + 2)}^{\frac{1}{3}})}^{3}$ .

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Step 2.3.2.1.1

Apply the product rule to $2 {(x + 2)}^{\frac{1}{3}}$ .

$2^{3} {({(x + 2)}^{\frac{1}{3}})}^{3} = 4^{3}$

Step 2.3.2.1.2

Raise $2$ to the power of $3$ .

$8 {({(x + 2)}^{\frac{1}{3}})}^{3} = 4^{3}$

Step 2.3.2.1.3

Multiply the exponents in ${({(x + 2)}^{\frac{1}{3}})}^{3}$ .

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Step 2.3.2.1.3.1

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

$8 {(x + 2)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Step 2.3.2.1.3.2

Cancel the common factor of $3$ .

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Step 2.3.2.1.3.2.1

Cancel the common factor.

$8 {(x + 2)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Step 2.3.2.1.3.2.2

Rewrite the expression.

$8 {(x + 2)}^{1} = 4^{3}$

Step 2.3.2.1.4

Simplify.

$8 (x + 2) = 4^{3}$

Step 2.3.2.1.5

Apply the distributive property.

$8 x + 8 \cdot 2 = 4^{3}$

Step 2.3.2.1.6

Multiply $8$ by $2$ .

$8 x + 16 = 4^{3}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

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

$8 x + 16 = 64$

Step 2.4

Solve for $x$ .

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Step 2.4.1

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

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Step 2.4.1.1

Subtract $16$ from both sides of the equation.

$8 x = 64 - 16$

Step 2.4.1.2

Subtract $16$ from $64$ .

$8 x = 48$

Step 2.4.2

Divide each term in $8 x = 48$ by $8$ and simplify.

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Step 2.4.2.1

Divide each term in $8 x = 48$ by $8$ .

$\frac{8 x}{8} = \frac{48}{8}$

Step 2.4.2.2

Simplify the left side.

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Step 2.4.2.2.1

Cancel the common factor of $8$ .

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Step 2.4.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{48}{8}$

Step 2.4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{48}{8}$

Step 2.4.2.3

Simplify the right side.

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Step 2.4.2.3.1

Divide $48$ by $8$ .

$x = 6$

Step 3