Solve for x - cube root of 5-2x=1

$- \sqrt[3]{5 - 2 x} = 1$

Step 1

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

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

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5 - 2 x}$ as ${(5 - 2 x)}^{\frac{1}{3}}$ .

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

Simplify the left side.

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

Apply the product rule to $- {(5 - 2 x)}^{\frac{1}{3}}$ .

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

Raise $- 1$ to the power of $3$ .

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

Multiply the exponents in ${({(5 - 2 x)}^{\frac{1}{3}})}^{3}$ .

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Apply the distributive property.

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

Multiply.

Multiply $- 1$ by $5$ .

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

Multiply $- 2$ by $- 1$ .

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

Simplify the right side.

One to any power is one.

$- 5 + 2 x = 1$

Step 3

Solve for $x$ .

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

Add $5$ to both sides of the equation.

$2 x = 1 + 5$

Add $1$ and $5$ .

$2 x = 6$

Divide each term in $2 x = 6$ by $2$ and simplify.

Divide each term in $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$x = 3$

Solve for x - cube root of 5-2x=1

Related Questions

Support LCMGCF.com by disabling your adblocker.