Finite Math Examples

$f (x) = \sqrt[1]{5 - 4 x}$

Step 1

Set $\sqrt[1]{5 - 4 x}$ equal to $0$ .

$\sqrt[1]{5 - 4 x} = 0$

Step 2

Solve for $x$ .

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Step 2.1

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $1$ .

${\sqrt[1]{5 - 4 x}}^{1} = 0^{1}$

Step 2.2

Simplify each side of the equation.

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Step 2.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[1]{5 - 4 x}$ as ${(5 - 4 x)}^{\frac{1}{1}}$ .

${({(5 - 4 x)}^{\frac{1}{1}})}^{1} = 0^{1}$

Step 2.2.2

Divide $1$ by $1$ .

${({(5 - 4 x)}^{1})}^{1} = 0^{1}$

Step 2.2.3

Simplify the left side.

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Step 2.2.3.1

Simplify ${({(5 - 4 x)}^{1})}^{1}$ .

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Step 2.2.3.1.1

Multiply the exponents in ${({(5 - 4 x)}^{1})}^{1}$ .

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Step 2.2.3.1.1.1

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

${(5 - 4 x)}^{1 \cdot 1} = 0^{1}$

Step 2.2.3.1.1.2

Multiply $1$ by $1$ .

${(5 - 4 x)}^{1} = 0^{1}$

Step 2.2.3.1.2

Simplify.

$5 - 4 x = 0^{1}$

Step 2.2.4

Simplify the right side.

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Step 2.2.4.1

Evaluate the exponent.

$5 - 4 x = 0$

Step 2.3

Solve for $x$ .

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Step 2.3.1

Subtract $5$ from both sides of the equation.

$- 4 x = - 5$

Step 2.3.2

Divide each term in $- 4 x = - 5$ by $- 4$ and simplify.

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Step 2.3.2.1

Divide each term in $- 4 x = - 5$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 5}{- 4}$

Step 2.3.2.2

Simplify the left side.

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Step 2.3.2.2.1

Cancel the common factor of $- 4$ .

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Step 2.3.2.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 5}{- 4}$

Step 2.3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 5}{- 4}$

Step 2.3.2.3

Simplify the right side.

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Step 2.3.2.3.1

Dividing two negative values results in a positive value.

$x = \frac{5}{4}$

Step 3