Algebra Examples

$3 \sqrt[3]{x + 1} = 2$

Step 1

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

${(3 \sqrt[3]{x + 1})}^{3} = 2^{3}$

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

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

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

Step 2.2.1.2

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

$27 {({(x + 1)}^{\frac{1}{3}})}^{3} = 2^{3}$

Step 2.2.1.3

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

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Step 2.2.1.3.1

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

$27 {(x + 1)}^{\frac{1}{3} \cdot 3} = 2^{3}$

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.

$27 {(x + 1)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Step 2.2.1.3.2.2

Rewrite the expression.

$27 {(x + 1)}^{1} = 2^{3}$

Step 2.2.1.4

Simplify.

$27 (x + 1) = 2^{3}$

Step 2.2.1.5

Apply the distributive property.

$27 x + 27 \cdot 1 = 2^{3}$

Step 2.2.1.6

Multiply $27$ by $1$ .

$27 x + 27 = 2^{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

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

$27 x + 27 = 8$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $27$ from both sides of the equation.

$27 x = 8 - 27$

Step 3.1.2

Subtract $27$ from $8$ .

$27 x = - 19$

Step 3.2

Divide each term in $27 x = - 19$ by $27$ and simplify.

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Step 3.2.1

Divide each term in $27 x = - 19$ by $27$ .

$\frac{27 x}{27} = \frac{- 19}{27}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $27$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{27 x}{27} = \frac{- 19}{27}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 19}{27}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$x = - \frac{19}{27}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{19}{27}$

Decimal Form:

$x = - 0.\overline{703}$