Solve by Factoring cube root of 4x+7=4

$\sqrt[3]{4 x + 7} = 4$

Step 1

Subtract $4$ from both sides of the equation.

$\sqrt[3]{4 x + 7} - 4 = 0$

Step 2

Add $4$ to both sides of the equation.

$\sqrt[3]{4 x + 7} = 4$

Step 3

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

${\sqrt[3]{4 x + 7}}^{3} = 4^{3}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4 x + 7}$ as ${(4 x + 7)}^{\frac{1}{3}}$ .

${({(4 x + 7)}^{\frac{1}{3}})}^{3} = 4^{3}$

Simplify the left side.

Simplify ${({(4 x + 7)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(4 x + 7)}^{\frac{1}{3}})}^{3}$ .

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

${(4 x + 7)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(4 x + 7)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Rewrite the expression.

${(4 x + 7)}^{1} = 4^{3}$

Simplify.

$4 x + 7 = 4^{3}$

Simplify the right side.

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

$4 x + 7 = 64$

Step 5

Solve for $x$ .

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

Subtract $7$ from both sides of the equation.

$4 x = 64 - 7$

Subtract $7$ from $64$ .

$4 x = 57$

Divide each term in $4 x = 57$ by $4$ and simplify.

Divide each term in $4 x = 57$ by $4$ .

$\frac{4 x}{4} = \frac{57}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{57}{4}$

Divide $x$ by $1$ .

$x = \frac{57}{4}$