Solve for x 2 cube root of 3x+1-11=-3

$2 \sqrt[3]{3 x + 1} - 11 = - 3$

Move all terms not containing $2 \sqrt[3]{3 x + 1}$ to the right side of the equation.

Add $11$ to both sides of the equation.

$2 \sqrt[3]{3 x + 1} = - 3 + 11$

Add $- 3$ and $11$ .

$2 \sqrt[3]{3 x + 1} = 8$

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

${(2 \sqrt[3]{3 x + 1})}^{3} = 8^{3}$

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

$8 {({(3 x + 1)}^{\frac{1}{3}})}^{3} = 8^{3}$

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

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

$8 {(3 x + 1)}^{\frac{1}{3} \cdot 3} = 8^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$8 {(3 x + 1)}^{\frac{1}{3} \cdot 3} = 8^{3}$

Rewrite the expression.

$8 {(3 x + 1)}^{1} = 8^{3}$

Simplify.

$8 (3 x + 1) = 8^{3}$

Apply the distributive property.

$8 (3 x) + 8 \cdot 1 = 8^{3}$

Multiply.

Multiply $3$ by $8$ .

$24 x + 8 \cdot 1 = 8^{3}$

Multiply $8$ by $1$ .

$24 x + 8 = 8^{3}$

Simplify the right side.

Raise $8$ to the power of $3$ .

$24 x + 8 = 512$

Solve for $x$ .

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

Subtract $8$ from both sides of the equation.

$24 x = 512 - 8$

Subtract $8$ from $512$ .

$24 x = 504$

Divide each term in $24 x = 504$ by $24$ and simplify.

Divide each term in $24 x = 504$ by $24$ .

$\frac{24 x}{24} = \frac{504}{24}$

Simplify the left side.

Cancel the common factor of $24$ .

Cancel the common factor.

$\frac{24 x}{24} = \frac{504}{24}$

Divide $x$ by $1$ .

$x = \frac{504}{24}$

Simplify the right side.

Divide $504$ by $24$ .

$x = 21$

Solve for x 2 cube root of 3x+1-11=-3

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