Algebra Examples

${(3 x - 21)}^{\frac{1}{3}} = {(19 - x)}^{\frac{1}{3}}$

Step 1

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$3 x - 21 = 19 - x$

Step 2

Solve for $x$ .

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Step 2.1

Move all terms containing $x$ to the left side of the equation.

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Step 2.1.1

Add $x$ to both sides of the equation.

$3 x - 21 + x = 19$

Step 2.1.2

Add $3 x$ and $x$ .

$4 x - 21 = 19$

Step 2.2

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

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Step 2.2.1

Add $21$ to both sides of the equation.

$4 x = 19 + 21$

Step 2.2.2

Add $19$ and $21$ .

$4 x = 40$

Step 2.3

Divide each term in $4 x = 40$ by $4$ and simplify.

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Step 2.3.1

Divide each term in $4 x = 40$ by $4$ .

$\frac{4 x}{4} = \frac{40}{4}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $4$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{40}{4}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{40}{4}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $40$ by $4$ .

$x = 10$