Algebra Examples

$q = \frac{x^{3}}{3} + y$

Step 1

Rewrite the equation as $\frac{x^{3}}{3} + y = q$ .

$\frac{x^{3}}{3} + y = q$

Step 2

Subtract $y$ from both sides of the equation.

$\frac{x^{3}}{3} = q - y$

Step 3

Multiply both sides of the equation by $3$ .

$3 \frac{x^{3}}{3} = 3 (q - y)$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1

Cancel the common factor.

$3 \frac{x^{3}}{3} = 3 (q - y)$

Step 4.1.1.2

Rewrite the expression.

$x^{3} = 3 (q - y)$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $3 (q - y)$ .

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Step 4.2.1.1

Apply the distributive property.

$x^{3} = 3 q + 3 (- y)$

Step 4.2.1.2

Multiply $- 1$ by $3$ .

$x^{3} = 3 q - 3 y$

Step 5

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[3]{3 q - 3 y}$

Step 6

Factor $3$ out of $3 q - 3 y$ .

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Step 6.1

Factor $3$ out of $3 q$ .

$x = \sqrt[3]{3 (q) - 3 y}$

Step 6.2

Factor $3$ out of $- 3 y$ .

$x = \sqrt[3]{3 (q) + 3 (- y)}$

Step 6.3

Factor $3$ out of $3 (q) + 3 (- y)$ .

$x = \sqrt[3]{3 (q - y)}$