Solve for x cube root of 1/4x+3=2

$\sqrt[3]{\frac{1}{4} x + 3} = 2$

Step 1

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

${\sqrt[3]{\frac{1}{4} x + 3}}^{3} = 2^{3}$

Step 2

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Combine $\frac{1}{4}$ and $x$ .

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

Simplify.

$\frac{x}{4} + 3 = 2^{3}$

Simplify the right side.

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

$\frac{x}{4} + 3 = 8$

Step 3

Solve for $x$ .

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

Subtract $3$ from both sides of the equation.

$\frac{x}{4} = 8 - 3$

Subtract $3$ from $8$ .

$\frac{x}{4} = 5$

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 \cdot 5$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{x}{4} = 4 \cdot 5$

Rewrite the expression.

$x = 4 \cdot 5$

Simplify the right side.

Multiply $4$ by $5$ .

$x = 20$