Solve for x -2 cube root of x-1 = cube root of x-10

$- 2 \sqrt[3]{x - 1} = \sqrt[3]{x - 10}$

Step 1

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

${(- 2 \sqrt[3]{x - 1})}^{3} = {\sqrt[3]{x - 10}}^{3}$

Step 2

Simplify each side of the equation.

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

${(- 2 {(x - 1)}^{\frac{1}{3}})}^{3} = {\sqrt[3]{x - 10}}^{3}$

Simplify the left side.

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

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

${(- 2)}^{3} {({(x - 1)}^{\frac{1}{3}})}^{3} = {\sqrt[3]{x - 10}}^{3}$

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

$- 8 {({(x - 1)}^{\frac{1}{3}})}^{3} = {\sqrt[3]{x - 10}}^{3}$

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

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

$- 8 {(x - 1)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{x - 10}}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 8 {(x - 1)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{x - 10}}^{3}$

Rewrite the expression.

$- 8 {(x - 1)}^{1} = {\sqrt[3]{x - 10}}^{3}$

Simplify.

$- 8 (x - 1) = {\sqrt[3]{x - 10}}^{3}$

Apply the distributive property.

$- 8 x - 8 \cdot - 1 = {\sqrt[3]{x - 10}}^{3}$

Multiply $- 8$ by $- 1$ .

$- 8 x + 8 = {\sqrt[3]{x - 10}}^{3}$

Simplify the right side.

Rewrite ${\sqrt[3]{x - 10}}^{3}$ as $x - 10$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x - 10}$ as ${(x - 10)}^{\frac{1}{3}}$ .

$- 8 x + 8 = {({(x - 10)}^{\frac{1}{3}})}^{3}$

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

$- 8 x + 8 = {(x - 10)}^{\frac{1}{3} \cdot 3}$

Combine $\frac{1}{3}$ and $3$ .

$- 8 x + 8 = {(x - 10)}^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 8 x + 8 = {(x - 10)}^{\frac{3}{3}}$

Rewrite the expression.

$- 8 x + 8 = {(x - 10)}^{1}$

Simplify.

$- 8 x + 8 = x - 10$

Step 3

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$- 8 x + 8 - x = - 10$

Subtract $x$ from $- 8 x$ .

$- 9 x + 8 = - 10$

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

Subtract $8$ from both sides of the equation.

$- 9 x = - 10 - 8$

Subtract $8$ from $- 10$ .

$- 9 x = - 18$

Divide each term in $- 9 x = - 18$ by $- 9$ and simplify.

Divide each term in $- 9 x = - 18$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{- 18}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{- 18}{- 9}$

Divide $x$ by $1$ .

$x = \frac{- 18}{- 9}$

Simplify the right side.

Divide $- 18$ by $- 9$ .

$x = 2$

Solve for x -2 cube root of x-1 = cube root of x-10

Related Questions

Support LCMGCF.com by disabling your adblocker.