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

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

Step 1

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

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 $9 (x) + 9 (- 1)$ .

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

Step 2

Add $3$ to both sides of the equation.

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

Step 3

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

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

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{9 (x - 1)}$ as ${(9 (x - 1))}^{\frac{1}{3}}$ .

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

Simplify the left side.

Simplify ${({(9 (x - 1))}^{\frac{1}{3}})}^{3}$ .

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

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 $3$ .

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.

Multiply $9$ by $- 1$ .

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

Simplify.

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

Simplify the right side.

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

$9 x - 9 = 27$

Step 5

Solve for $x$ .

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

Add $9$ to both sides of the equation.

$9 x = 27 + 9$

Add $27$ and $9$ .

$9 x = 36$

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

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

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

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $36$ by $9$ .

$x = 4$

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

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