Algebra Examples

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

Step 1

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

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Step 1.1

Add $5$ to both sides of the equation.

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

Step 1.2

Add $- 4$ and $5$ .

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

Step 2

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

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

Step 3

Simplify the exponent.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify ${(\frac{1}{4} \cdot {(x + 2)}^{\frac{1}{3}})}^{3}$ .

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Step 3.1.1.1

Combine fractions.

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Step 3.1.1.1.1

Combine $\frac{1}{4}$ and ${(x + 2)}^{\frac{1}{3}}$ .

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

Step 3.1.1.1.2

Apply the product rule to $\frac{{(x + 2)}^{\frac{1}{3}}}{4}$ .

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

Step 3.1.1.2

Simplify the numerator.

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Step 3.1.1.2.1

Multiply the exponents in ${({(x + 2)}^{\frac{1}{3}})}^{3}$ .

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Step 3.1.1.2.1.1

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

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

Step 3.1.1.2.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.2.1.2.1

Cancel the common factor.

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

Step 3.1.1.2.1.2.2

Rewrite the expression.

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

Step 3.1.1.2.2

Simplify.

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

Step 3.1.1.3

Raise $4$ to the power of $3$ .

$\frac{x + 2}{64} = 1^{3}$

Step 3.1.1.4

Split the fraction $\frac{x + 2}{64}$ into two fractions.

$\frac{x}{64} + \frac{2}{64} = 1^{3}$

Step 3.1.1.5

Cancel the common factor of $2$ and $64$ .

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Step 3.1.1.5.1

Factor $2$ out of $2$ .

$\frac{x}{64} + \frac{2 (1)}{64} = 1^{3}$

Step 3.1.1.5.2

Cancel the common factors.

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Step 3.1.1.5.2.1

Factor $2$ out of $64$ .

$\frac{x}{64} + \frac{2 \cdot 1}{2 \cdot 32} = 1^{3}$

Step 3.1.1.5.2.2

Cancel the common factor.

$\frac{x}{64} + \frac{2 \cdot 1}{2 \cdot 32} = 1^{3}$

Step 3.1.1.5.2.3

Rewrite the expression.

$\frac{x}{64} + \frac{1}{32} = 1^{3}$

Step 3.2

Simplify the right side.

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Step 3.2.1

One to any power is one.

$\frac{x}{64} + \frac{1}{32} = 1$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $\frac{1}{32}$ from both sides of the equation.

$\frac{x}{64} = 1 - \frac{1}{32}$

Step 4.1.2

Write $1$ as a fraction with a common denominator.

$\frac{x}{64} = \frac{32}{32} - \frac{1}{32}$

Step 4.1.3

Combine the numerators over the common denominator.

$\frac{x}{64} = \frac{32 - 1}{32}$

Step 4.1.4

Subtract $1$ from $32$ .

$\frac{x}{64} = \frac{31}{32}$

Step 4.2

Multiply both sides of the equation by $64$ .

$64 \frac{x}{64} = 64 (\frac{31}{32})$

Step 4.3

Simplify both sides of the equation.

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Step 4.3.1

Simplify the left side.

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Step 4.3.1.1

Cancel the common factor of $64$ .

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Step 4.3.1.1.1

Cancel the common factor.

$64 \frac{x}{64} = 64 (\frac{31}{32})$

Step 4.3.1.1.2

Rewrite the expression.

$x = 64 (\frac{31}{32})$

Step 4.3.2

Simplify the right side.

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Step 4.3.2.1

Simplify $64 (\frac{31}{32})$ .

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Step 4.3.2.1.1

Cancel the common factor of $32$ .

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Step 4.3.2.1.1.1

Factor $32$ out of $64$ .

$x = 32 (2) \frac{31}{32}$

Step 4.3.2.1.1.2

Cancel the common factor.

$x = 32 \cdot 2 \frac{31}{32}$

Step 4.3.2.1.1.3

Rewrite the expression.

$x = 2 \cdot 31$

Step 4.3.2.1.2

Multiply $2$ by $31$ .

$x = 62$