Algebra Examples

$12 - \sqrt[3]{2 x - 7} = 21$

Step 1

Move all terms not containing $- \sqrt[3]{2 x - 7}$ to the right side of the equation.

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Step 1.1

Subtract $12$ from both sides of the equation.

$- \sqrt[3]{2 x - 7} = 21 - 12$

Step 1.2

Subtract $12$ from $21$ .

$- \sqrt[3]{2 x - 7} = 9$

Step 2

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

${(- \sqrt[3]{2 x - 7})}^{3} = 9^{3}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 x - 7}$ as ${(2 x - 7)}^{\frac{1}{3}}$ .

${(- {(2 x - 7)}^{\frac{1}{3}})}^{3} = 9^{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(- {(2 x - 7)}^{\frac{1}{3}})}^{3}$ .

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Step 3.2.1.1

Apply the product rule to $- {(2 x - 7)}^{\frac{1}{3}}$ .

${(- 1)}^{3} {({(2 x - 7)}^{\frac{1}{3}})}^{3} = 9^{3}$

Step 3.2.1.2

Raise $- 1$ to the power of $3$ .

$- {({(2 x - 7)}^{\frac{1}{3}})}^{3} = 9^{3}$

Step 3.2.1.3

Multiply the exponents in ${({(2 x - 7)}^{\frac{1}{3}})}^{3}$ .

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Step 3.2.1.3.1

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

$- {(2 x - 7)}^{\frac{1}{3} \cdot 3} = 9^{3}$

Step 3.2.1.3.2

Cancel the common factor of $3$ .

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Step 3.2.1.3.2.1

Cancel the common factor.

$- {(2 x - 7)}^{\frac{1}{3} \cdot 3} = 9^{3}$

Step 3.2.1.3.2.2

Rewrite the expression.

$- {(2 x - 7)}^{1} = 9^{3}$

Step 3.2.1.4

Simplify.

$- (2 x - 7) = 9^{3}$

Step 3.2.1.5

Apply the distributive property.

$- (2 x) - - 7 = 9^{3}$

Step 3.2.1.6

Multiply.

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Step 3.2.1.6.1

Multiply $2$ by $- 1$ .

$- 2 x - - 7 = 9^{3}$

Step 3.2.1.6.2

Multiply $- 1$ by $- 7$ .

$- 2 x + 7 = 9^{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $9$ to the power of $3$ .

$- 2 x + 7 = 729$

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 $7$ from both sides of the equation.

$- 2 x = 729 - 7$

Step 4.1.2

Subtract $7$ from $729$ .

$- 2 x = 722$

Step 4.2

Divide each term in $- 2 x = 722$ by $- 2$ and simplify.

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Step 4.2.1

Divide each term in $- 2 x = 722$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{722}{- 2}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{722}{- 2}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{722}{- 2}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $722$ by $- 2$ .

$x = - 361$

Step 5