Solve by Factoring cube root of 3x-2=-5

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

Step 1

Add $5$ to both sides of the equation.

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

Step 2

Subtract $5$ from both sides of the equation.

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

Step 3

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

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

Step 4

Simplify each side of the equation.

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

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

Simplify the left side.

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

Multiply the exponents in ${({(3 x - 2)}^{\frac{1}{3}})}^{3}$ .

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Raise $- 5$ to the power of $3$ .

$3 x - 2 = - 125$

Step 5

Solve for $x$ .

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

Add $2$ to both sides of the equation.

$3 x = - 125 + 2$

Add $- 125$ and $2$ .

$3 x = - 123$

Divide each term in $3 x = - 123$ by $3$ and simplify.

Divide each term in $3 x = - 123$ by $3$ .

$\frac{3 x}{3} = \frac{- 123}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 123}{3}$

Divide $x$ by $1$ .

$x = \frac{- 123}{3}$

Simplify the right side.

Divide $- 123$ by $3$ .

$x = - 41$

Solve by Factoring cube root of 3x-2=-5

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