Solve by Factoring cube root of 5x-1+6=10

$\sqrt[3]{5 x - 1} + 6 = 10$

Step 1

Subtract $10$ from both sides of the equation.

$\sqrt[3]{5 x - 1} + 6 - 10 = 0$

Step 2

Subtract $10$ from $6$ .

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

Step 3

Add $4$ to both sides of the equation.

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

Step 4

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

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

Step 5

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Raise $4$ to the power of $3$ .

$5 x - 1 = 64$

Step 6

Solve for $x$ .

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

Add $1$ to both sides of the equation.

$5 x = 64 + 1$

Add $64$ and $1$ .

$5 x = 65$

Divide each term in $5 x = 65$ by $5$ and simplify.

Divide each term in $5 x = 65$ by $5$ .

$\frac{5 x}{5} = \frac{65}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{65}{5}$

Divide $x$ by $1$ .

$x = \frac{65}{5}$

Simplify the right side.

Divide $65$ by $5$ .

$x = 13$

Solve by Factoring cube root of 5x-1+6=10

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