Algebra Examples

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

Step 1

Set $- \sqrt[3]{x + 1} - 1$ equal to $0$ .

$- \sqrt[3]{x + 1} - 1 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $1$ to both sides of the equation.

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

Step 2.2

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

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

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

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

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

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

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Step 2.3.2.1.1

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

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

Step 2.3.2.1.2

Raise $- 1$ to the power of $3$ .

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

Step 2.3.2.1.3

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

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Step 2.3.2.1.3.1

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

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

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.

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

Step 2.3.2.1.3.2.2

Rewrite the expression.

$- {(x + 1)}^{1} = 1^{3}$

Step 2.3.2.1.4

Simplify.

$- (x + 1) = 1^{3}$

Step 2.3.2.1.5

Apply the distributive property.

$- x - 1 \cdot 1 = 1^{3}$

Step 2.3.2.1.6

Multiply $- 1$ by $1$ .

$- x - 1 = 1^{3}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

One to any power is one.

$- x - 1 = 1$

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

Add $1$ to both sides of the equation.

$- x = 1 + 1$

Step 2.4.1.2

Add $1$ and $1$ .

$- x = 2$

Step 2.4.2

Divide each term in $- x = 2$ by $- 1$ and simplify.

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Step 2.4.2.1

Divide each term in $- x = 2$ by $- 1$ .

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

Step 2.4.2.2

Simplify the left side.

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Step 2.4.2.2.1

Dividing two negative values results in a positive value.

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

Step 2.4.2.2.2

Divide $x$ by $1$ .

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

Step 2.4.2.3

Simplify the right side.

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Step 2.4.2.3.1

Divide $2$ by $- 1$ .

$x = - 2$

Step 3