Finite Math Examples

$n = 6$ , $y = 4 x^{3} - 1$

Step 1

Solve the equation for $x$ .

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Step 1.1

Rewrite the equation as $4 x^{3} - 1 = y$ .

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

$n = 6$

Step 1.2

Add $1$ to both sides of the equation.

$4 x^{3} = y + 1$

$n = 6$

Step 1.3

Divide each term in $4 x^{3} = y + 1$ by $4$ and simplify.

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Step 1.3.1

Divide each term in $4 x^{3} = y + 1$ by $4$ .

$\frac{4 x^{3}}{4} = \frac{y}{4} + \frac{1}{4}$

$n = 6$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $4$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{4 x^{3}}{4} = \frac{y}{4} + \frac{1}{4}$

$n = 6$

Step 1.3.2.1.2

Divide $x^{3}$ by $1$ .

$x^{3} = \frac{y}{4} + \frac{1}{4}$

$n = 6$

$x^{3} = \frac{y}{4} + \frac{1}{4}$

$n = 6$

$x^{3} = \frac{y}{4} + \frac{1}{4}$

$n = 6$

$x^{3} = \frac{y}{4} + \frac{1}{4}$

$n = 6$

Step 1.4

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

$x = \sqrt[3]{\frac{y}{4} + \frac{1}{4}}$

$n = 6$

Step 1.5

Simplify $\sqrt[3]{\frac{y}{4} + \frac{1}{4}}$ .

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Step 1.5.1

Combine the numerators over the common denominator.

$x = \sqrt[3]{\frac{y + 1}{4}}$

$n = 6$

Step 1.5.2

Rewrite $\sqrt[3]{\frac{y + 1}{4}}$ as $\frac{\sqrt[3]{y + 1}}{\sqrt[3]{4}}$ .

$x = \frac{\sqrt[3]{y + 1}}{\sqrt[3]{4}}$

$n = 6$

Step 1.5.3

Multiply $\frac{\sqrt[3]{y + 1}}{\sqrt[3]{4}}$ by $\frac{{\sqrt[3]{4}}^{2}}{{\sqrt[3]{4}}^{2}}$ .

$x = \frac{\sqrt[3]{y + 1}}{\sqrt[3]{4}} \cdot \frac{{\sqrt[3]{4}}^{2}}{{\sqrt[3]{4}}^{2}}$

$n = 6$

Step 1.5.4

Combine and simplify the denominator.

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Step 1.5.4.1

Multiply $\frac{\sqrt[3]{y + 1}}{\sqrt[3]{4}}$ by $\frac{{\sqrt[3]{4}}^{2}}{{\sqrt[3]{4}}^{2}}$ .

$x = \frac{\sqrt[3]{y + 1} {\sqrt[3]{4}}^{2}}{\sqrt[3]{4} {\sqrt[3]{4}}^{2}}$

$n = 6$

Step 1.5.4.2

Raise $\sqrt[3]{4}$ to the power of $1$ .

$x = \frac{\sqrt[3]{y + 1} {\sqrt[3]{4}}^{2}}{\sqrt[3]{4} {\sqrt[3]{4}}^{2}}$

$n = 6$

Step 1.5.4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \frac{\sqrt[3]{y + 1} {\sqrt[3]{4}}^{2}}{{\sqrt[3]{4}}^{1 + 2}}$

$n = 6$

Step 1.5.4.4

Add $1$ and $2$ .

$x = \frac{\sqrt[3]{y + 1} {\sqrt[3]{4}}^{2}}{{\sqrt[3]{4}}^{3}}$

$n = 6$

Step 1.5.4.5

Rewrite ${\sqrt[3]{4}}^{3}$ as $4$ .

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Step 1.5.4.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4}$ as $4^{\frac{1}{3}}$ .

$x = \frac{\sqrt[3]{y + 1} {\sqrt[3]{4}}^{2}}{{(4^{\frac{1}{3}})}^{3}}$

$n = 6$

Step 1.5.4.5.2

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

$x = \frac{\sqrt[3]{y + 1} {\sqrt[3]{4}}^{2}}{4^{\frac{1}{3} \cdot 3}}$

$n = 6$

Step 1.5.4.5.3

Combine $\frac{1}{3}$ and $3$ .

$x = \frac{\sqrt[3]{y + 1} {\sqrt[3]{4}}^{2}}{4^{\frac{3}{3}}}$

$n = 6$

Step 1.5.4.5.4

Cancel the common factor of $3$ .

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Step 1.5.4.5.4.1

Cancel the common factor.

$x = \frac{\sqrt[3]{y + 1} {\sqrt[3]{4}}^{2}}{4^{\frac{3}{3}}}$

$n = 6$

Step 1.5.4.5.4.2

Rewrite the expression.