Algebra Examples

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

Step 1

Move all terms not containing $\sqrt[3]{5 x - 6}$ to the right side of the equation.

Tap for more steps...

Step 1.1

Subtract $3$ from both sides of the equation.

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

Step 1.2

Subtract $3$ from $4$ .

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

Step 2

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

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

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 $\sqrt[3]{5 x - 6}$ as ${(5 x - 6)}^{\frac{1}{3}}$ .

${({(5 x - 6)}^{\frac{1}{3}})}^{3} = 1^{3}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Simplify ${({(5 x - 6)}^{\frac{1}{3}})}^{3}$ .

Tap for more steps...

Step 3.2.1.1

Multiply the exponents in ${({(5 x - 6)}^{\frac{1}{3}})}^{3}$ .

Tap for more steps...

Step 3.2.1.1.1

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

${(5 x - 6)}^{\frac{1}{3} \cdot 3} = 1^{3}$

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.

${(5 x - 6)}^{\frac{1}{3} \cdot 3} = 1^{3}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(5 x - 6)}^{1} = 1^{3}$

Step 3.2.1.2

Simplify.

$5 x - 6 = 1^{3}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

One to any power is one.

$5 x - 6 = 1$

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 $6$ to both sides of the equation.

$5 x = 1 + 6$

Step 4.1.2

Add $1$ and $6$ .

$5 x = 7$

Step 4.2

Divide each term in $5 x = 7$ by $5$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $5 x = 7$ by $5$ .

$\frac{5 x}{5} = \frac{7}{5}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{7}{5}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{7}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{5}$

Decimal Form:

$x = 1.4$

Mixed Number Form:

$x = 1 \frac{2}{5}$