Algebra Examples

$11 \sqrt[3]{3 - 2 x} - 6 = 60$

Step 1

Move all terms not containing $11 \sqrt[3]{3 - 2 x}$ to the right side of the equation.

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Step 1.1

Add $6$ to both sides of the equation.

$11 \sqrt[3]{3 - 2 x} = 60 + 6$

Step 1.2

Add $60$ and $6$ .

$11 \sqrt[3]{3 - 2 x} = 66$

Step 2

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

${(11 \sqrt[3]{3 - 2 x})}^{3} = 66^{3}$

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 $\sqrt[3]{3 - 2 x}$ as ${(3 - 2 x)}^{\frac{1}{3}}$ .

${(11 {(3 - 2 x)}^{\frac{1}{3}})}^{3} = 66^{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(11 {(3 - 2 x)}^{\frac{1}{3}})}^{3}$ .

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Step 3.2.1.1

Apply the product rule to $11 {(3 - 2 x)}^{\frac{1}{3}}$ .

$11^{3} {({(3 - 2 x)}^{\frac{1}{3}})}^{3} = 66^{3}$

Step 3.2.1.2

Raise $11$ to the power of $3$ .

$1331 {({(3 - 2 x)}^{\frac{1}{3}})}^{3} = 66^{3}$

Step 3.2.1.3

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

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Step 3.2.1.3.1

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

$1331 {(3 - 2 x)}^{\frac{1}{3} \cdot 3} = 66^{3}$

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.

$1331 {(3 - 2 x)}^{\frac{1}{3} \cdot 3} = 66^{3}$

Step 3.2.1.3.2.2

Rewrite the expression.

$1331 {(3 - 2 x)}^{1} = 66^{3}$

Step 3.2.1.4

Simplify.

$1331 (3 - 2 x) = 66^{3}$

Step 3.2.1.5

Apply the distributive property.

$1331 \cdot 3 + 1331 (- 2 x) = 66^{3}$

Step 3.2.1.6

Multiply.

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Step 3.2.1.6.1

Multiply $1331$ by $3$ .

$3993 + 1331 (- 2 x) = 66^{3}$

Step 3.2.1.6.2

Multiply $- 2$ by $1331$ .

$3993 - 2662 x = 66^{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $66$ to the power of $3$ .

$3993 - 2662 x = 287496$

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 $3993$ from both sides of the equation.

$- 2662 x = 287496 - 3993$

Step 4.1.2

Subtract $3993$ from $287496$ .

$- 2662 x = 283503$

Step 4.2

Divide each term in $- 2662 x = 283503$ by $- 2662$ and simplify.

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Step 4.2.1

Divide each term in $- 2662 x = 283503$ by $- 2662$ .

$\frac{- 2662 x}{- 2662} = \frac{283503}{- 2662}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $- 2662$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{- 2662 x}{- 2662} = \frac{283503}{- 2662}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{283503}{- 2662}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Cancel the common factor of $283503$ and $- 2662$ .

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Step 4.2.3.1.1

Factor $1331$ out of $283503$ .

$x = \frac{1331 (213)}{- 2662}$

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

Factor $1331$ out of $- 2662$ .

$x = \frac{1331 \cdot 213}{1331 \cdot - 2}$

Step 4.2.3.1.2.2

Cancel the common factor.

$x = \frac{1331 \cdot 213}{1331 \cdot - 2}$

Step 4.2.3.1.2.3

Rewrite the expression.

$x = \frac{213}{- 2}$

Step 4.2.3.2

Move the negative in front of the fraction.

$x = - \frac{213}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{213}{2}$

Decimal Form:

$x = - 106.5$

Mixed Number Form:

$x = - 106 \frac{1}{2}$