Algebra Examples

$\sqrt[3]{7 x - 1} = - 2$

Step 1

Add $2$ to both sides of the equation.

$\sqrt[3]{7 x - 1} + 2 = 0$

Step 2

Subtract $2$ from both sides of the equation.

$\sqrt[3]{7 x - 1} = - 2$

Step 3

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

${\sqrt[3]{7 x - 1}}^{3} = {(- 2)}^{3}$

Step 4

Simplify each side of the equation.

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Step 4.1

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

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

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Step 4.2.1.1

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

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Step 4.2.1.1.1

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

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

Step 4.2.1.1.2

Cancel the common factor of $3$ .

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Step 4.2.1.1.2.1

Cancel the common factor.

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

Step 4.2.1.1.2.2

Rewrite the expression.

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

Step 4.2.1.2

Simplify.

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

Step 4.3

Simplify the right side.

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Step 4.3.1

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

$7 x - 1 = - 8$

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 $1$ to both sides of the equation.

$7 x = - 8 + 1$

Step 5.1.2

Add $- 8$ and $1$ .

$7 x = - 7$

Step 5.2

Divide each term in $7 x = - 7$ by $7$ and simplify.

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Step 5.2.1

Divide each term in $7 x = - 7$ by $7$ .

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

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $7$ .

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Step 5.2.2.1.1

Cancel the common factor.

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

Step 5.2.2.1.2

Divide $x$ by $1$ .

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

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $- 7$ by $7$ .

$x = - 1$