Solve by Factoring cube root of 3x-3=2

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

Step 1

Subtract $2$ from both sides of the equation.

$\sqrt[3]{3 x - 3} - 2 = 0$

Step 2

Factor $3$ out of $3 x - 3$ .

Factor $3$ out of $3 x$ .

$\sqrt[3]{3 (x) - 3} - 2 = 0$

Factor $3$ out of $- 3$ .

$\sqrt[3]{3 (x) + 3 (- 1)} - 2 = 0$

Factor $3$ out of $3 (x) + 3 (- 1)$ .

$\sqrt[3]{3 (x - 1)} - 2 = 0$

Step 3

Add $2$ to both sides of the equation.

$\sqrt[3]{3 (x - 1)} = 2$

Step 4

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

${\sqrt[3]{3 (x - 1)}}^{3} = 2^{3}$

Step 5

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

${(3 (x - 1))}^{1} = 2^{3}$

Apply the distributive property.

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

Multiply.

Multiply $3$ by $- 1$ .

${(3 x - 3)}^{1} = 2^{3}$

Simplify.

$3 x - 3 = 2^{3}$

Simplify the right side.

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

$3 x - 3 = 8$

Step 6

Solve for $x$ .

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

Add $3$ to both sides of the equation.

$3 x = 8 + 3$

Add $8$ and $3$ .

$3 x = 11$

Divide each term in $3 x = 11$ by $3$ and simplify.

Divide each term in $3 x = 11$ by $3$ .

$\frac{3 x}{3} = \frac{11}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{11}{3}$

Divide $x$ by $1$ .

$x = \frac{11}{3}$

Solve by Factoring cube root of 3x-3=2

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