Solve for x cube root of 6x-5- cube root of 3x+2=0

$\sqrt[3]{6 x - 5} - \sqrt[3]{3 x + 2} = 0$

Step 1

Add $\sqrt[3]{3 x + 2}$ to both sides of the equation.

$\sqrt[3]{6 x - 5} = \sqrt[3]{3 x + 2}$

Step 2

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

${\sqrt[3]{6 x - 5}}^{3} = {\sqrt[3]{3 x + 2}}^{3}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{6 x - 5}$ as ${(6 x - 5)}^{\frac{1}{3}}$ .

${({(6 x - 5)}^{\frac{1}{3}})}^{3} = {\sqrt[3]{3 x + 2}}^{3}$

Simplify the left side.

Simplify ${({(6 x - 5)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(6 x - 5)}^{\frac{1}{3}})}^{3}$ .

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

${(6 x - 5)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{3 x + 2}}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(6 x - 5)}^{\frac{1}{3} \cdot 3} = {\sqrt[3]{3 x + 2}}^{3}$

Rewrite the expression.

${(6 x - 5)}^{1} = {\sqrt[3]{3 x + 2}}^{3}$

Simplify.

$6 x - 5 = {\sqrt[3]{3 x + 2}}^{3}$

Simplify the right side.

Rewrite ${\sqrt[3]{3 x + 2}}^{3}$ as $3 x + 2$ .

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

$6 x - 5 = {({(3 x + 2)}^{\frac{1}{3}})}^{3}$

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

$6 x - 5 = {(3 x + 2)}^{\frac{1}{3} \cdot 3}$

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

$6 x - 5 = {(3 x + 2)}^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$6 x - 5 = {(3 x + 2)}^{\frac{3}{3}}$

Rewrite the expression.

$6 x - 5 = {(3 x + 2)}^{1}$

Simplify.

$6 x - 5 = 3 x + 2$

Step 4

Solve for $x$ .

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

Subtract $3 x$ from both sides of the equation.

$6 x - 5 - 3 x = 2$

Subtract $3 x$ from $6 x$ .

$3 x - 5 = 2$

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

Add $5$ to both sides of the equation.

$3 x = 2 + 5$

Add $2$ and $5$ .

$3 x = 7$

Divide each term in $3 x = 7$ by $3$ and simplify.

Divide each term in $3 x = 7$ by $3$ .

$\frac{3 x}{3} = \frac{7}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{7}{3}$

Divide $x$ by $1$ .

$x = \frac{7}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{3}$

Decimal Form:

$x = 2.\overline{3}$

Mixed Number Form:

$x = 2 \frac{1}{3}$

Solve for x cube root of 6x-5- cube root of 3x+2=0

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