Algebra Examples

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

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.

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

Step 1.2

Add $3$ and $5$ .

$4 {(3 - x)}^{\frac{1}{3}} = 8$

Step 2

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

${(4 {(3 - x)}^{\frac{1}{3}})}^{3} = 8^{3}$

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 ${(4 {(3 - x)}^{\frac{1}{3}})}^{3}$ .

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Step 3.1.1.1

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

$4^{3} {({(3 - x)}^{\frac{1}{3}})}^{3} = 8^{3}$

Step 3.1.1.2

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

$64 {({(3 - x)}^{\frac{1}{3}})}^{3} = 8^{3}$

Step 3.1.1.3

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

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Step 3.1.1.3.1

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

$64 {(3 - x)}^{\frac{1}{3} \cdot 3} = 8^{3}$

Step 3.1.1.3.2

Cancel the common factor of $3$ .

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Step 3.1.1.3.2.1

Cancel the common factor.

$64 {(3 - x)}^{\frac{1}{3} \cdot 3} = 8^{3}$

Step 3.1.1.3.2.2

Rewrite the expression.

$64 {(3 - x)}^{1} = 8^{3}$

Step 3.1.1.4

Simplify.

$64 (3 - x) = 8^{3}$

Step 3.1.1.5

Apply the distributive property.

$64 \cdot 3 + 64 (- x) = 8^{3}$

Step 3.1.1.6

Multiply.

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Step 3.1.1.6.1

Multiply $64$ by $3$ .

$192 + 64 (- x) = 8^{3}$

Step 3.1.1.6.2

Multiply $- 1$ by $64$ .

$192 - 64 x = 8^{3}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Raise $8$ to the power of $3$ .

$192 - 64 x = 512$

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 $192$ from both sides of the equation.

$- 64 x = 512 - 192$

Step 4.1.2

Subtract $192$ from $512$ .

$- 64 x = 320$

Step 4.2

Divide each term in $- 64 x = 320$ by $- 64$ and simplify.

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Step 4.2.1

Divide each term in $- 64 x = 320$ by $- 64$ .

$\frac{- 64 x}{- 64} = \frac{320}{- 64}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 64$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 64 x}{- 64} = \frac{320}{- 64}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{320}{- 64}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $320$ by $- 64$ .

$x = - 5$