Solve by Factoring cube root of 4x-1=-5

$\sqrt[3]{4 x - 1} = - 5$

Step 1

Add $5$ to both sides of the equation.

$\sqrt[3]{4 x - 1} + 5 = 0$

Step 2

Subtract $5$ from both sides of the equation.

$\sqrt[3]{4 x - 1} = - 5$

Step 3

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

${\sqrt[3]{4 x - 1}}^{3} = {(- 5)}^{3}$

Step 4

Simplify each side of the equation.

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

${({(4 x - 1)}^{\frac{1}{3}})}^{3} = {(- 5)}^{3}$

Simplify the left side.

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

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

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

${(4 x - 1)}^{\frac{1}{3} \cdot 3} = {(- 5)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(4 x - 1)}^{\frac{1}{3} \cdot 3} = {(- 5)}^{3}$

Rewrite the expression.

${(4 x - 1)}^{1} = {(- 5)}^{3}$

Simplify.

$4 x - 1 = {(- 5)}^{3}$

Simplify the right side.

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

$4 x - 1 = - 125$

Step 5

Solve for $x$ .

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

Add $1$ to both sides of the equation.

$4 x = - 125 + 1$

Add $- 125$ and $1$ .

$4 x = - 124$

Divide each term in $4 x = - 124$ by $4$ and simplify.

Divide each term in $4 x = - 124$ by $4$ .

$\frac{4 x}{4} = \frac{- 124}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 124}{4}$

Divide $x$ by $1$ .

$x = \frac{- 124}{4}$

Simplify the right side.

Divide $- 124$ by $4$ .

$x = - 31$

Solve by Factoring cube root of 4x-1=-5

Related Questions

Support LCMGCF.com by disabling your adblocker.