Solve for x 5- cube root of x-4=2

$5 - \sqrt[3]{x - 4} = 2$

Move all terms not containing $- \sqrt[3]{x - 4}$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$- \sqrt[3]{x - 4} = 2 - 5$

Subtract $5$ from $2$ .

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

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

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

Simplify each side of the equation.

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

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

Simplify the left side.

Simplify ${(- {(x - 4)}^{\frac{1}{3}})}^{3}$ .

Apply the product rule to $- {(x - 4)}^{\frac{1}{3}}$ .

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

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

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

Multiply the exponents in ${({(x - 4)}^{\frac{1}{3}})}^{3}$ .

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$- {(x - 4)}^{1} = {(- 3)}^{3}$

Simplify.

$- (x - 4) = {(- 3)}^{3}$

Apply the distributive property.

$- x - - 4 = {(- 3)}^{3}$

Multiply $- 1$ by $- 4$ .

$- x + 4 = {(- 3)}^{3}$

Simplify the right side.

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

$- x + 4 = - 27$

Solve for $x$ .

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

Subtract $4$ from both sides of the equation.

$- x = - 27 - 4$

Subtract $4$ from $- 27$ .

$- x = - 31$

Divide each term in $- x = - 31$ by $- 1$ and simplify.

Divide each term in $- x = - 31$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 31}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 31}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 31}{- 1}$

Simplify the right side.

Divide $- 31$ by $- 1$ .

$x = 31$

Solve for x 5- cube root of x-4=2

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