Algebra Examples

$f (x) = \sqrt[3]{3 x - 7}$ , $f (x) = 2$

Step 1

Substitute $2$ for $f (x)$ .

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

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $\sqrt[3]{3 x - 7} = 2$ .

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

Step 2.2

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

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

Step 2.3

Simplify each side of the equation.

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Step 2.3.1

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

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

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

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

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Step 2.3.2.1.1

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

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Step 2.3.2.1.1.1

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

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

Step 2.3.2.1.1.2

Cancel the common factor of $3$ .

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Step 2.3.2.1.1.2.1

Cancel the common factor.

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

Step 2.3.2.1.1.2.2

Rewrite the expression.

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

Step 2.3.2.1.2

Simplify.

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

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

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

$3 x - 7 = 8$

Step 2.4

Solve for $x$ .

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Step 2.4.1

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

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Step 2.4.1.1

Add $7$ to both sides of the equation.

$3 x = 8 + 7$

Step 2.4.1.2

Add $8$ and $7$ .

$3 x = 15$

Step 2.4.2

Divide each term in $3 x = 15$ by $3$ and simplify.

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Step 2.4.2.1

Divide each term in $3 x = 15$ by $3$ .

$\frac{3 x}{3} = \frac{15}{3}$

Step 2.4.2.2

Simplify the left side.

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Step 2.4.2.2.1

Cancel the common factor of $3$ .

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Step 2.4.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{15}{3}$

Step 2.4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{15}{3}$

Step 2.4.2.3

Simplify the right side.

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Step 2.4.2.3.1

Divide $15$ by $3$ .

$x = 5$