Solve by Factoring cube root of 9x-9-3=0

$\sqrt[3]{9 x - 9} - 3 = 0$

Factor $9$ out of $9 x - 9$ .

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Factor $9$ out of $9 x$ .

$\sqrt[3]{9 (x) - 9} - 3 = 0$

Factor $9$ out of $- 9$ .

$\sqrt[3]{9 (x) + 9 (- 1)} - 3 = 0$

Factor $9$ out of $9 (x) + 9 (- 1)$ .

$\sqrt[3]{9 (x - 1)} - 3 = 0$

Add $3$ to both sides of the equation.

$\sqrt[3]{9 (x - 1)} = 3$

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

${\sqrt[3]{9 (x - 1)}}^{3} = 3^{3}$

Simplify each side of the equation.

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Multiply the exponents in ${({(9 (x - 1))}^{\frac{1}{3}})}^{3}$ .

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

${(9 (x - 1))}^{\frac{1}{3} \cdot 3} = 3^{3}$

Cancel the common factor of $3$ .

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Cancel the common factor.

${(9 (x - 1))}^{\frac{1}{3} \cdot 3} = 3^{3}$

Rewrite the expression.

${(9 (x - 1))}^{1} = 3^{3}$

Apply the distributive property.

${(9 x + 9 \cdot - 1)}^{1} = 3^{3}$

Multiply $9$ by $- 1$ .

${(9 x - 9)}^{1} = 3^{3}$

Simplify.

$9 x - 9 = 3^{3}$

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

$9 x - 9 = 27$

Solve for $x$ .

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

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Add $9$ to both sides of the equation.

$9 x = 27 + 9$

Add $27$ and $9$ .

$9 x = 36$

Divide each term by $9$ and simplify.

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Divide each term in $9 x = 36$ by $9$ .

$\frac{9 x}{9} = \frac{36}{9}$

Cancel the common factor of $9$ .

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Cancel the common factor.

$\frac{9 x}{9} = \frac{36}{9}$

Divide $x$ by $1$ .

$x = \frac{36}{9}$

Divide $36$ by $9$ .

$x = 4$

Solve by Factoring cube root of 9x-9-3=0

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