Solve the Rational Equation for x (3x-21)^(1/3)=(19-x)^(1/3)

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

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 $x$ .

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

Add $x$ to both sides of the equation.

$3 x - 21 + x = 19$

Add $3 x$ and $x$ .

$4 x - 21 = 19$

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

Add $21$ to both sides of the equation.

$4 x = 19 + 21$

Add $19$ and $21$ .

$4 x = 40$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $40$ by $4$ .

$x = 10$