Solve by Factoring cube root of 5x+4+5=6

$\sqrt[3]{5 x + 4} + 5 = 6$

Step 1

Subtract $6$ from both sides of the equation.

$\sqrt[3]{5 x + 4} + 5 - 6 = 0$

Step 2

Subtract $6$ from $5$ .

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

Step 3

Add $1$ to both sides of the equation.

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

Step 4

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

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

Step 5

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5 x + 4}$ as ${(5 x + 4)}^{\frac{1}{3}}$ .

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

Simplify the left side.

Simplify ${({(5 x + 4)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(5 x + 4)}^{\frac{1}{3}})}^{3}$ .

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$5 x + 4 = 1^{3}$

Simplify the right side.

One to any power is one.

$5 x + 4 = 1$

Step 6

Solve for $x$ .

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

Subtract $4$ from both sides of the equation.

$5 x = 1 - 4$

Subtract $4$ from $1$ .

$5 x = - 3$

Divide each term in $5 x = - 3$ by $5$ and simplify.

Divide each term in $5 x = - 3$ by $5$ .

$\frac{5 x}{5} = \frac{- 3}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 3}{5}$

Divide $x$ by $1$ .

$x = \frac{- 3}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{5}$

Solve by Factoring cube root of 5x+4+5=6

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