Solve for x -2 cube root of 2x+10-1=3

$- 2 \sqrt[3]{2 x + 10} - 1 = 3$

Move all terms not containing $- 2 \sqrt[3]{2 x + 10}$ to the right side of the equation.

Add $1$ to both sides of the equation.

$- 2 \sqrt[3]{2 x + 10} = 3 + 1$

Add $3$ and $1$ .

$- 2 \sqrt[3]{2 x + 10} = 4$

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

${(- 2 \sqrt[3]{2 x + 10})}^{3} = 4^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 x + 10}$ as ${(2 x + 10)}^{\frac{1}{3}}$ .

${(- 2 {(2 x + 10)}^{\frac{1}{3}})}^{3} = 4^{3}$

Simplify the left side.

Simplify ${(- 2 {(2 x + 10)}^{\frac{1}{3}})}^{3}$ .

Apply the product rule to $- 2 {(2 x + 10)}^{\frac{1}{3}}$ .

${(- 2)}^{3} {({(2 x + 10)}^{\frac{1}{3}})}^{3} = 4^{3}$

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

$- 8 {({(2 x + 10)}^{\frac{1}{3}})}^{3} = 4^{3}$

Multiply the exponents in ${({(2 x + 10)}^{\frac{1}{3}})}^{3}$ .

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

$- 8 {(2 x + 10)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 8 {(2 x + 10)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Rewrite the expression.

$- 8 {(2 x + 10)}^{1} = 4^{3}$

Simplify.

$- 8 (2 x + 10) = 4^{3}$

Apply the distributive property.

$- 8 (2 x) - 8 \cdot 10 = 4^{3}$

Multiply.

Multiply $2$ by $- 8$ .

$- 16 x - 8 \cdot 10 = 4^{3}$

Multiply $- 8$ by $10$ .

$- 16 x - 80 = 4^{3}$

Simplify the right side.

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

$- 16 x - 80 = 64$

Solve for $x$ .

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

Add $80$ to both sides of the equation.

$- 16 x = 64 + 80$

Add $64$ and $80$ .

$- 16 x = 144$

Divide each term in $- 16 x = 144$ by $- 16$ and simplify.

Divide each term in $- 16 x = 144$ by $- 16$ .

$\frac{- 16 x}{- 16} = \frac{144}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 x}{- 16} = \frac{144}{- 16}$

Divide $x$ by $1$ .

$x = \frac{144}{- 16}$

Simplify the right side.

Divide $144$ by $- 16$ .

$x = - 9$

Solve for x -2 cube root of 2x+10-1=3

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