Solve for x 4 = cube root of 6x+10

$4 = \sqrt[3]{6 x + 10}$

Step 1

Rewrite the equation as $\sqrt[3]{6 x + 10} = 4$ .

$\sqrt[3]{6 x + 10} = 4$

Step 2

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

${\sqrt[3]{6 x + 10}}^{3} = 4^{3}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{6 x + 10}$ as ${(6 x + 10)}^{\frac{1}{3}}$ .

${({(6 x + 10)}^{\frac{1}{3}})}^{3} = 4^{3}$

Simplify the left side.

Simplify ${({(6 x + 10)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(6 x + 10)}^{\frac{1}{3}})}^{3}$ .

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

${(6 x + 10)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(6 x + 10)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Rewrite the expression.

${(6 x + 10)}^{1} = 4^{3}$

Simplify.

$6 x + 10 = 4^{3}$

Simplify the right side.

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

$6 x + 10 = 64$

Step 4

Solve for $x$ .

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

Subtract $10$ from both sides of the equation.

$6 x = 64 - 10$

Subtract $10$ from $64$ .

$6 x = 54$

Divide each term in $6 x = 54$ by $6$ and simplify.

Divide each term in $6 x = 54$ by $6$ .

$\frac{6 x}{6} = \frac{54}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{54}{6}$

Divide $x$ by $1$ .

$x = \frac{54}{6}$

Simplify the right side.

Divide $54$ by $6$ .

$x = 9$