Solve for x cube root of 4x-9 = cube root of 2x-4

$\sqrt[3]{4 x - 9} = \sqrt[3]{2 x - 4}$

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

${\sqrt[3]{4 x - 9}}^{3} = {\sqrt[3]{2 x - 4}}^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4 x - 9}$ as ${(4 x - 9)}^{\frac{1}{3}}$ .

${({(4 x - 9)}^{\frac{1}{3}})}^{3} = {\sqrt[3]{2 x - 4}}^{3}$

Simplify the left side.

Simplify ${({(4 x - 9)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(4 x - 9)}^{\frac{1}{3}})}^{3}$ .

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

${(4 x - 9)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{2 x - 4}}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(4 x - 9)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{2 x - 4}}^{3}$

Rewrite the expression.

${(4 x - 9)}^{1} = {\sqrt[3]{2 x - 4}}^{3}$

Simplify.

$4 x - 9 = {\sqrt[3]{2 x - 4}}^{3}$

Simplify the right side.

Simplify ${\sqrt[3]{2 x - 4}}^{3}$ .

Factor $2$ out of $2 x - 4$ .

Factor $2$ out of $2 x$ .

$4 x - 9 = {\sqrt[3]{2 (x) - 4}}^{3}$

Factor $2$ out of $- 4$ .

$4 x - 9 = {\sqrt[3]{2 x + 2 \cdot - 2}}^{3}$

Factor $2$ out of $2 x + 2 \cdot - 2$ .

$4 x - 9 = {\sqrt[3]{2 (x - 2)}}^{3}$

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

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

$4 x - 9 = {({(2 (x - 2))}^{\frac{1}{3}})}^{3}$

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

$4 x - 9 = {(2 (x - 2))}^{\frac{1}{3} \cdot 3}$

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

$4 x - 9 = {(2 (x - 2))}^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$4 x - 9 = {(2 (x - 2))}^{\frac{3}{3}}$

Rewrite the expression.

$4 x - 9 = {(2 (x - 2))}^{1}$

Simplify.

$4 x - 9 = 2 (x - 2)$

Apply the distributive property.

$4 x - 9 = 2 x + 2 \cdot - 2$

Multiply $2$ by $- 2$ .

$4 x - 9 = 2 x - 4$

Solve for $x$ .

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

Subtract $2 x$ from both sides of the equation.

$4 x - 9 - 2 x = - 4$

Subtract $2 x$ from $4 x$ .

$2 x - 9 = - 4$

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

Add $9$ to both sides of the equation.

$2 x = - 4 + 9$

Add $- 4$ and $9$ .

$2 x = 5$

Divide each term in $2 x = 5$ by $2$ and simplify.

Divide each term in $2 x = 5$ by $2$ .

$\frac{2 x}{2} = \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{5}{2}$

Divide $x$ by $1$ .

$x = \frac{5}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{2}$

Decimal Form:

$x = 2.5$

Mixed Number Form:

$x = 2 \frac{1}{2}$

Solve for x cube root of 4x-9 = cube root of 2x-4

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