Solve for x cube root of 8x- cube root of 6x-2=0

$\sqrt[3]{8 x} - \sqrt[3]{6 x - 2} = 0$

Step 1

Solve for $\sqrt[3]{8 x}$ .

Factor $2$ out of $6 x - 2$ .

Factor $2$ out of $6 x$ .

$\sqrt[3]{8 x} - \sqrt[3]{2 (3 x) - 2} = 0$

Factor $2$ out of $- 2$ .

$\sqrt[3]{8 x} - \sqrt[3]{2 (3 x) + 2 (- 1)} = 0$

Factor $2$ out of $2 (3 x) + 2 (- 1)$ .

$\sqrt[3]{8 x} - \sqrt[3]{2 (3 x - 1)} = 0$

Add $\sqrt[3]{2 (3 x - 1)}$ to both sides of the equation.

$\sqrt[3]{8 x} = \sqrt[3]{2 (3 x - 1)}$

Step 2

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

${\sqrt[3]{8 x}}^{3} = {\sqrt[3]{2 (3 x - 1)}}^{3}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{8 x}$ as ${(8 x)}^{\frac{1}{3}}$ .

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

Simplify the left side.

Simplify ${({(8 x)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(8 x)}^{\frac{1}{3}})}^{3}$ .

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

${(8 x)}^{1} = {\sqrt[3]{2 (3 x - 1)}}^{3}$

Simplify.

$8 x = {\sqrt[3]{2 (3 x - 1)}}^{3}$

Simplify the right side.

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

Rewrite ${\sqrt[3]{2 (3 x - 1)}}^{3}$ as $2 (3 x - 1)$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 (3 x - 1)}$ as ${(2 (3 x - 1))}^{\frac{1}{3}}$ .

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

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$8 x = 2 (3 x - 1)$

Apply the distributive property.

$8 x = 2 (3 x) + 2 \cdot - 1$

Multiply.

Multiply $3$ by $2$ .

$8 x = 6 x + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$8 x = 6 x - 2$

Step 4

Solve for $x$ .

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

Subtract $6 x$ from both sides of the equation.

$8 x - 6 x = - 2$

Subtract $6 x$ from $8 x$ .

$2 x = - 2$

Divide each term in $2 x = - 2$ by $2$ and simplify.

Divide each term in $2 x = - 2$ by $2$ .

$\frac{2 x}{2} = \frac{- 2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 2}{2}$

Divide $x$ by $1$ .

$x = \frac{- 2}{2}$

Simplify the right side.

Divide $- 2$ by $2$ .

$x = - 1$

Solve for x cube root of 8x- cube root of 6x-2=0

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