Algebra Examples

$2 {(x - 5)}^{\frac{1}{3}} - 3 = 7$

Step 1

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

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Step 1.1

Add $3$ to both sides of the equation.

$2 {(x - 5)}^{\frac{1}{3}} = 7 + 3$

Step 1.2

Add $7$ and $3$ .

$2 {(x - 5)}^{\frac{1}{3}} = 10$

Step 2

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

${(2 {(x - 5)}^{\frac{1}{3}})}^{3} = 10^{3}$

Step 3

Simplify the exponent.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify ${(2 {(x - 5)}^{\frac{1}{3}})}^{3}$ .

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Step 3.1.1.1

Apply the product rule to $2 {(x - 5)}^{\frac{1}{3}}$ .

$2^{3} {({(x - 5)}^{\frac{1}{3}})}^{3} = 10^{3}$

Step 3.1.1.2

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

$8 {({(x - 5)}^{\frac{1}{3}})}^{3} = 10^{3}$

Step 3.1.1.3

Multiply the exponents in ${({(x - 5)}^{\frac{1}{3}})}^{3}$ .

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Step 3.1.1.3.1

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

$8 {(x - 5)}^{\frac{1}{3} \cdot 3} = 10^{3}$

Step 3.1.1.3.2

Cancel the common factor of $3$ .

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Step 3.1.1.3.2.1

Cancel the common factor.

$8 {(x - 5)}^{\frac{1}{3} \cdot 3} = 10^{3}$

Step 3.1.1.3.2.2

Rewrite the expression.

$8 {(x - 5)}^{1} = 10^{3}$

Step 3.1.1.4

Simplify.

$8 (x - 5) = 10^{3}$

Step 3.1.1.5

Apply the distributive property.

$8 x + 8 \cdot - 5 = 10^{3}$

Step 3.1.1.6

Multiply $8$ by $- 5$ .

$8 x - 40 = 10^{3}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Raise $10$ to the power of $3$ .

$8 x - 40 = 1000$

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

Add $40$ to both sides of the equation.

$8 x = 1000 + 40$

Step 4.1.2

Add $1000$ and $40$ .

$8 x = 1040$

Step 4.2

Divide each term in $8 x = 1040$ by $8$ and simplify.

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Step 4.2.1

Divide each term in $8 x = 1040$ by $8$ .

$\frac{8 x}{8} = \frac{1040}{8}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $8$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{1040}{8}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1040}{8}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $1040$ by $8$ .

$x = 130$