Solve for x 3-2 cube root of x-1=5

$3 - 2 \sqrt[3]{x - 1} = 5$

Step 1

Move all terms not containing $- 2 \sqrt[3]{x - 1}$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$- 2 \sqrt[3]{x - 1} = 5 - 3$

Subtract $3$ from $5$ .

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

Step 2

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

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

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

Apply the product rule to $- 2 {(x - 1)}^{\frac{1}{3}}$ .

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

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

$- 8 {({(x - 1)}^{\frac{1}{3}})}^{3} = 2^{3}$

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

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

$- 8 {(x - 1)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 8 {(x - 1)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Rewrite the expression.

$- 8 {(x - 1)}^{1} = 2^{3}$

Simplify.

$- 8 (x - 1) = 2^{3}$

Apply the distributive property.

$- 8 x - 8 \cdot - 1 = 2^{3}$

Multiply $- 8$ by $- 1$ .

$- 8 x + 8 = 2^{3}$

Simplify the right side.

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

$- 8 x + 8 = 8$

Step 4

Solve for $x$ .

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

Subtract $8$ from both sides of the equation.

$- 8 x = 8 - 8$

Subtract $8$ from $8$ .

$- 8 x = 0$

Divide each term in $- 8 x = 0$ by $- 8$ and simplify.

Divide each term in $- 8 x = 0$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{0}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{0}{- 8}$

Divide $x$ by $1$ .

$x = \frac{0}{- 8}$

Simplify the right side.

Divide $0$ by $- 8$ .

$x = 0$

Solve for x 3-2 cube root of x-1=5

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