Solve for x 1=5+ cube root of 5x-14

$1 = 5 + \sqrt[3]{5 x - 14}$

Rewrite the equation as $5 + \sqrt[3]{5 x - 14} = 1$ .

$5 + \sqrt[3]{5 x - 14} = 1$

Move all terms not containing $\sqrt[3]{5 x - 14}$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$\sqrt[3]{5 x - 14} = 1 - 5$

Subtract $5$ from $1$ .

$\sqrt[3]{5 x - 14} = - 4$

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

${\sqrt[3]{5 x - 14}}^{3} = {(- 4)}^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5 x - 14}$ as ${(5 x - 14)}^{\frac{1}{3}}$ .

${({(5 x - 14)}^{\frac{1}{3}})}^{3} = {(- 4)}^{3}$

Simplify the left side.

Simplify ${({(5 x - 14)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(5 x - 14)}^{\frac{1}{3}})}^{3}$ .

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

${(5 x - 14)}^{\frac{1}{3} \cdot 3} = {(- 4)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(5 x - 14)}^{\frac{1}{3} \cdot 3} = {(- 4)}^{3}$

Rewrite the expression.

${(5 x - 14)}^{1} = {(- 4)}^{3}$

Simplify.

$5 x - 14 = {(- 4)}^{3}$

Simplify the right side.

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

$5 x - 14 = - 64$

Solve for $x$ .

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

Add $14$ to both sides of the equation.

$5 x = - 64 + 14$

Add $- 64$ and $14$ .

$5 x = - 50$

Divide each term in $5 x = - 50$ by $5$ and simplify.

Divide each term in $5 x = - 50$ by $5$ .

$\frac{5 x}{5} = \frac{- 50}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 50}{5}$

Divide $x$ by $1$ .

$x = \frac{- 50}{5}$

Simplify the right side.

Divide $- 50$ by $5$ .

$x = - 10$

Solve for x 1=5+ cube root of 5x-14

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