Algebra Examples

$10 = 18 - 4 {(29 - 7 x)}^{\frac{1}{3}}$

Step 1

Rewrite the equation as $18 - 4 {(29 - 7 x)}^{\frac{1}{3}} = 10$ .

$18 - 4 {(29 - 7 x)}^{\frac{1}{3}} = 10$

Step 2

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

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Step 2.1

Subtract $18$ from both sides of the equation.

$- 4 {(29 - 7 x)}^{\frac{1}{3}} = 10 - 18$

Step 2.2

Subtract $18$ from $10$ .

$- 4 {(29 - 7 x)}^{\frac{1}{3}} = - 8$

Step 3

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

${(- 4 {(29 - 7 x)}^{\frac{1}{3}})}^{3} = {(- 8)}^{3}$

Step 4

Simplify the exponent.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify ${(- 4 {(29 - 7 x)}^{\frac{1}{3}})}^{3}$ .

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Step 4.1.1.1

Apply the product rule to $- 4 {(29 - 7 x)}^{\frac{1}{3}}$ .

${(- 4)}^{3} {({(29 - 7 x)}^{\frac{1}{3}})}^{3} = {(- 8)}^{3}$

Step 4.1.1.2

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

$- 64 {({(29 - 7 x)}^{\frac{1}{3}})}^{3} = {(- 8)}^{3}$

Step 4.1.1.3

Multiply the exponents in ${({(29 - 7 x)}^{\frac{1}{3}})}^{3}$ .

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Step 4.1.1.3.1

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

$- 64 {(29 - 7 x)}^{\frac{1}{3} \cdot 3} = {(- 8)}^{3}$

Step 4.1.1.3.2

Cancel the common factor of $3$ .

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Step 4.1.1.3.2.1

Cancel the common factor.

$- 64 {(29 - 7 x)}^{\frac{1}{3} \cdot 3} = {(- 8)}^{3}$

Step 4.1.1.3.2.2

Rewrite the expression.

$- 64 {(29 - 7 x)}^{1} = {(- 8)}^{3}$

Step 4.1.1.4

Simplify.

$- 64 (29 - 7 x) = {(- 8)}^{3}$

Step 4.1.1.5

Apply the distributive property.

$- 64 \cdot 29 - 64 (- 7 x) = {(- 8)}^{3}$

Step 4.1.1.6

Multiply.

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Step 4.1.1.6.1

Multiply $- 64$ by $29$ .

$- 1856 - 64 (- 7 x) = {(- 8)}^{3}$

Step 4.1.1.6.2

Multiply $- 7$ by $- 64$ .

$- 1856 + 448 x = {(- 8)}^{3}$

Step 4.2

Simplify the right side.

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Step 4.2.1

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

$- 1856 + 448 x = - 512$

Step 5

Solve for $x$ .

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Step 5.1

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

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Step 5.1.1

Add $1856$ to both sides of the equation.

$448 x = - 512 + 1856$

Step 5.1.2

Add $- 512$ and $1856$ .

$448 x = 1344$

Step 5.2

Divide each term in $448 x = 1344$ by $448$ and simplify.

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Step 5.2.1

Divide each term in $448 x = 1344$ by $448$ .

$\frac{448 x}{448} = \frac{1344}{448}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $448$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{448 x}{448} = \frac{1344}{448}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1344}{448}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $1344$ by $448$ .

$x = 3$