Solve for x (2x-3)^(1/3)=(x+5)^(1/3)

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

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

$2 x - 3 = x + 5$

Solve for $x$ .

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

Subtract $x$ from both sides of the equation.

$2 x - 3 - x = 5$

Subtract $x$ from $2 x$ .

$x - 3 = 5$

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

Add $3$ to both sides of the equation.

$x = 5 + 3$

Add $5$ and $3$ .

$x = 8$