Solve for x cube root of 4x+1-2=2

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

Move all terms not containing $\sqrt[3]{4 x + 1}$ to the right side of the equation.

Add $2$ to both sides of the equation.

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

Add $2$ and $2$ .

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

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

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

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$4 x + 1 = 4^{3}$

Simplify the right side.

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

$4 x + 1 = 64$

Solve for $x$ .

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

Subtract $1$ from both sides of the equation.

$4 x = 64 - 1$

Subtract $1$ from $64$ .

$4 x = 63$

Divide each term in $4 x = 63$ by $4$ and simplify.

Divide each term in $4 x = 63$ by $4$ .

$\frac{4 x}{4} = \frac{63}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{63}{4}$

Divide $x$ by $1$ .

$x = \frac{63}{4}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{63}{4}$

Decimal Form:

$x = 15.75$

Mixed Number Form:

$x = 15 \frac{3}{4}$

Solve for x cube root of 4x+1-2=2

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