Algebra Examples

$- 8 + \sqrt[3]{2 x - 27} = - 5$

Step 1

Move all terms not containing $\sqrt[3]{2 x - 27}$ to the right side of the equation.

Tap for more steps...

Step 1.1

Add $8$ to both sides of the equation.

$\sqrt[3]{2 x - 27} = - 5 + 8$

Step 1.2

Add $- 5$ and $8$ .

$\sqrt[3]{2 x - 27} = 3$

Step 2

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

${\sqrt[3]{2 x - 27}}^{3} = 3^{3}$

Step 3

Simplify each side of the equation.

Tap for more steps...

Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 x - 27}$ as ${(2 x - 27)}^{\frac{1}{3}}$ .

${({(2 x - 27)}^{\frac{1}{3}})}^{3} = 3^{3}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Simplify ${({(2 x - 27)}^{\frac{1}{3}})}^{3}$ .

Tap for more steps...

Step 3.2.1.1

Multiply the exponents in ${({(2 x - 27)}^{\frac{1}{3}})}^{3}$ .

Tap for more steps...

Step 3.2.1.1.1

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

${(2 x - 27)}^{\frac{1}{3} \cdot 3} = 3^{3}$

Step 3.2.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.1.1.2.1

Cancel the common factor.

${(2 x - 27)}^{\frac{1}{3} \cdot 3} = 3^{3}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(2 x - 27)}^{1} = 3^{3}$

Step 3.2.1.2

Simplify.

$2 x - 27 = 3^{3}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

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

$2 x - 27 = 27$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Add $27$ to both sides of the equation.

$2 x = 27 + 27$

Step 4.1.2

Add $27$ and $27$ .

$2 x = 54$

Step 4.2

Divide each term in $2 x = 54$ by $2$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $2 x = 54$ by $2$ .

$\frac{2 x}{2} = \frac{54}{2}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{54}{2}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{54}{2}$

Step 4.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.3.1

Divide $54$ by $2$ .

$x = 27$