Solve for x 2 = cube root of 4x-12

$2 = \sqrt[3]{4 x - 12}$

Step 1

Rewrite the equation as $\sqrt[3]{4 x - 12} = 2$ .

$\sqrt[3]{4 x - 12} = 2$

Step 2

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

${\sqrt[3]{4 x - 12}}^{3} = 2^{3}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4 x - 12}$ as ${(4 x - 12)}^{\frac{1}{3}}$ .

${({(4 x - 12)}^{\frac{1}{3}})}^{3} = 2^{3}$

Simplify the left side.

Simplify ${({(4 x - 12)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(4 x - 12)}^{\frac{1}{3}})}^{3}$ .

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

${(4 x - 12)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(4 x - 12)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Rewrite the expression.

${(4 x - 12)}^{1} = 2^{3}$

Simplify.

$4 x - 12 = 2^{3}$

Simplify the right side.

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

$4 x - 12 = 8$

Step 4

Solve for $x$ .

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

Add $12$ to both sides of the equation.

$4 x = 8 + 12$

Add $8$ and $12$ .

$4 x = 20$

Divide each term in $4 x = 20$ by $4$ and simplify.

Divide each term in $4 x = 20$ by $4$ .

$\frac{4 x}{4} = \frac{20}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{20}{4}$

Divide $x$ by $1$ .

$x = \frac{20}{4}$

Simplify the right side.

Divide $20$ by $4$ .

$x = 5$