Finite Math Examples

$3 x + 5 y^{5} = - 14$

Step 1

Solve the equation for $y$ .

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Step 1.1

Subtract $3 x$ from both sides of the equation.

$5 y^{5} = - 14 - 3 x$

Step 1.2

Divide each term in $5 y^{5} = - 14 - 3 x$ by $5$ and simplify.

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Step 1.2.1

Divide each term in $5 y^{5} = - 14 - 3 x$ by $5$ .

$\frac{5 y^{5}}{5} = \frac{- 14}{5} + \frac{- 3 x}{5}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $5$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{5 y^{5}}{5} = \frac{- 14}{5} + \frac{- 3 x}{5}$

Step 1.2.2.1.2

Divide $y^{5}$ by $1$ .

$y^{5} = \frac{- 14}{5} + \frac{- 3 x}{5}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Move the negative in front of the fraction.

$y^{5} = - \frac{14}{5} + \frac{- 3 x}{5}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y^{5} = - \frac{14}{5} - \frac{3 x}{5}$

Step 1.3

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

$y = \sqrt[5]{- \frac{14}{5} - \frac{3 x}{5}}$

Step 1.4

Simplify $\sqrt[5]{- \frac{14}{5} - \frac{3 x}{5}}$ .

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Step 1.4.1

Factor $- 1$ out of $- \frac{14}{5} - \frac{3 x}{5}$ .

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Step 1.4.1.1

Reorder $- \frac{14}{5}$ and $- \frac{3 x}{5}$ .

$y = \sqrt[5]{- \frac{3 x}{5} - \frac{14}{5}}$

Step 1.4.1.2

Factor $- 1$ out of $- \frac{3 x}{5}$ .

$y = \sqrt[5]{- (\frac{3 x}{5}) - \frac{14}{5}}$

Step 1.4.1.3

Factor $- 1$ out of $- \frac{14}{5}$ .

$y = \sqrt[5]{- (\frac{3 x}{5}) - (\frac{14}{5})}$

Step 1.4.1.4

Factor $- 1$ out of $- (\frac{3 x}{5}) - (\frac{14}{5})$ .

$y = \sqrt[5]{- (\frac{3 x}{5} + \frac{14}{5})}$

Step 1.4.2

Combine the numerators over the common denominator.

$y = \sqrt[5]{- \frac{3 x + 14}{5}}$

Step 1.4.3

Rewrite $- \frac{3 x + 14}{5}$ as ${({(- 1)}^{5})}^{5} \frac{3 x + 14}{5}$ .

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Step 1.4.3.1

Rewrite $- 1$ as ${(- 1)}^{5}$ .

$y = \sqrt[5]{{(- 1)}^{5} \frac{3 x + 14}{5}}$

Step 1.4.3.2

Rewrite $- 1$ as ${(- 1)}^{5}$ .

$y = \sqrt[5]{{({(- 1)}^{5})}^{5} \frac{3 x + 14}{5}}$

Step 1.4.4

Pull terms out from under the radical.

$y = {(- 1)}^{5} \sqrt[5]{\frac{3 x + 14}{5}}$

Step 1.4.5

Raise $- 1$ to the power of $5$ .

$y = - \sqrt[5]{\frac{3 x + 14}{5}}$

Step 1.4.6

Rewrite $\sqrt[5]{\frac{3 x + 14}{5}}$ as $\frac{\sqrt[5]{3 x + 14}}{\sqrt[5]{5}}$ .

$y = - \frac{\sqrt[5]{3 x + 14}}{\sqrt[5]{5}}$

Step 1.4.7

Multiply $\frac{\sqrt[5]{3 x + 14}}{\sqrt[5]{5}}$ by $\frac{{\sqrt[5]{5}}^{4}}{{\sqrt[5]{5}}^{4}}$ .

$y = - (\frac{\sqrt[5]{3 x + 14}}{\sqrt[5]{5}} \cdot \frac{{\sqrt[5]{5}}^{4}}{{\sqrt[5]{5}}^{4}})$

Step 1.4.8

Combine and simplify the denominator.

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Step 1.4.8.1

Multiply $\frac{\sqrt[5]{3 x + 14}}{\sqrt[5]{5}}$ by $\frac{{\sqrt[5]{5}}^{4}}{{\sqrt[5]{5}}^{4}}$ .

$y = - \frac{\sqrt[5]{3 x + 14} {\sqrt[5]{5}}^{4}}{\sqrt[5]{5} {\sqrt[5]{5}}^{4}}$

Step 1.4.8.2

Raise $\sqrt[5]{5}$ to the power of $1$ .

$y = - \frac{\sqrt[5]{3 x + 14} {\sqrt[5]{5}}^{4}}{{\sqrt[5]{5}}^{1} {\sqrt[5]{5}}^{4}}$

Step 1.4.8.3

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

$y = - \frac{\sqrt[5]{3 x + 14} {\sqrt[5]{5}}^{4}}{{\sqrt[5]{5}}^{1 + 4}}$

Step 1.4.8.4

Add $1$ and $4$ .

$y = - \frac{\sqrt[5]{3 x + 14} {\sqrt[5]{5}}^{4}}{{\sqrt[5]{5}}^{5}}$

Step 1.4.8.5

Rewrite ${\sqrt[5]{5}}^{5}$ as $5$ .

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Step 1.4.8.5.1

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

$y = - \frac{\sqrt[5]{3 x + 14} {\sqrt[5]{5}}^{4}}{{(5^{\frac{1}{5}})}^{5}}$

Step 1.4.8.5.2

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

$y = - \frac{\sqrt[5]{3 x + 14} {\sqrt[5]{5}}^{4}}{5^{\frac{1}{5} \cdot 5}}$

Step 1.4.8.5.3

Combine $\frac{1}{5}$ and $5$ .

$y = - \frac{\sqrt[5]{3 x + 14} {\sqrt[5]{5}}^{4}}{5^{\frac{5}{5}}}$

Step 1.4.8.5.4

Cancel the common factor of $5$ .

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Step 1.4.8.5.4.1

Cancel the common factor.

$y = - \frac{\sqrt[5]{3 x + 14} {\sqrt[5]{5}}^{4}}{5^{\frac{5}{5}}}$

Step 1.4.8.5.4.2

Rewrite the expression.

$y = - \frac{\sqrt[5]{3 x + 14} {\sqrt[5]{5}}^{4}}{5^{1}}$

Step 1.4.8.5.5

Evaluate the exponent.

$y = - \frac{\sqrt[5]{3 x + 14} {\sqrt[5]{5}}^{4}}{5}$

Step 1.4.9

Simplify the numerator.

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Step 1.4.9.1

Rewrite ${\sqrt[5]{5}}^{4}$ as $\sqrt[5]{5^{4}}$ .

$y = - \frac{\sqrt[5]{3 x + 14} \sqrt[5]{5^{4}}}{5}$

Step 1.4.9.2

Raise $5$ to the power of $4$ .

$y = - \frac{\sqrt[5]{3 x + 14} \sqrt[5]{625}}{5}$

Step 1.4.10

Simplify with factoring out.

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Step 1.4.10.1

Combine using the product rule for radicals.

$y = - \frac{\sqrt[5]{(3 x + 14) \cdot 625}}{5}$

Step 1.4.10.2

Reorder factors in $- \frac{\sqrt[5]{(3 x + 14) \cdot 625}}{5}$ .

$y = - \frac{\sqrt[5]{625 (3 x + 14)}}{5}$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ , the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not a linear equation.

Not Linear