Algebra Examples

$\sqrt[3]{4 x + 5} = \frac{1}{2}$

Step 1

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

${\sqrt[3]{4 x + 5}}^{3} = {(\frac{1}{2})}^{3}$

Step 2

Simplify each side of the equation.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4 x + 5}$ as ${(4 x + 5)}^{\frac{1}{3}}$ .

${({(4 x + 5)}^{\frac{1}{3}})}^{3} = {(\frac{1}{2})}^{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(4 x + 5)}^{\frac{1}{3}})}^{3}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(4 x + 5)}^{\frac{1}{3}})}^{3}$ .

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Step 2.2.1.1.1

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

${(4 x + 5)}^{\frac{1}{3} \cdot 3} = {(\frac{1}{2})}^{3}$

Step 2.2.1.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(4 x + 5)}^{\frac{1}{3} \cdot 3} = {(\frac{1}{2})}^{3}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(4 x + 5)}^{1} = {(\frac{1}{2})}^{3}$

Step 2.2.1.2

Simplify.

$4 x + 5 = {(\frac{1}{2})}^{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify ${(\frac{1}{2})}^{3}$ .

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Step 2.3.1.1

Apply the product rule to $\frac{1}{2}$ .

$4 x + 5 = \frac{1^{3}}{2^{3}}$

Step 2.3.1.2

One to any power is one.

$4 x + 5 = \frac{1}{2^{3}}$

Step 2.3.1.3

Raise $2$ to the power of $3$ .

$4 x + 5 = \frac{1}{8}$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1.1

Subtract $5$ from both sides of the equation.

$4 x = \frac{1}{8} - 5$

Step 3.1.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$4 x = \frac{1}{8} - 5 \cdot \frac{8}{8}$

Step 3.1.3

Combine $- 5$ and $\frac{8}{8}$ .

$4 x = \frac{1}{8} + \frac{- 5 \cdot 8}{8}$

Step 3.1.4

Combine the numerators over the common denominator.

$4 x = \frac{1 - 5 \cdot 8}{8}$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Multiply $- 5$ by $8$ .

$4 x = \frac{1 - 40}{8}$

Step 3.1.5.2

Subtract $40$ from $1$ .

$4 x = \frac{- 39}{8}$

Step 3.1.6

Move the negative in front of the fraction.

$4 x = - \frac{39}{8}$

Step 3.2

Divide each term in $4 x = - \frac{39}{8}$ by $4$ and simplify.

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Step 3.2.1

Divide each term in $4 x = - \frac{39}{8}$ by $4$ .

$\frac{4 x}{4} = \frac{- \frac{39}{8}}{4}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{- \frac{39}{8}}{4}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{39}{8}}{4}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{39}{8} \cdot \frac{1}{4}$

Step 3.2.3.2

Multiply $- \frac{39}{8} \cdot \frac{1}{4}$ .

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Step 3.2.3.2.1

Multiply $\frac{1}{4}$ by $\frac{39}{8}$ .

$x = - \frac{39}{4 \cdot 8}$

Step 3.2.3.2.2

Multiply $4$ by $8$ .

$x = - \frac{39}{32}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{39}{32}$

Decimal Form:

$x = - 1.21875$

Mixed Number Form:

$x = - 1 \frac{7}{32}$