Solve the Rational Equation for x (-2x+6)^(1/5)=(-8+10x)^(1/5)

${(- 2 x + 6)}^{\frac{1}{5}} = {(- 8 + 10 x)}^{\frac{1}{5}}$

Step 1

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

$- 2 x + 6 = - 8 + 10 x$

Step 2

Solve for $x$ .

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

Subtract $10 x$ from both sides of the equation.

$- 2 x + 6 - 10 x = - 8$

Subtract $10 x$ from $- 2 x$ .

$- 12 x + 6 = - 8$

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

Subtract $6$ from both sides of the equation.

$- 12 x = - 8 - 6$

Subtract $6$ from $- 8$ .

$- 12 x = - 14$

Divide each term in $- 12 x = - 14$ by $- 12$ and simplify.

Divide each term in $- 12 x = - 14$ by $- 12$ .

$\frac{- 12 x}{- 12} = \frac{- 14}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 x}{- 12} = \frac{- 14}{- 12}$

Divide $x$ by $1$ .

$x = \frac{- 14}{- 12}$

Simplify the right side.

Cancel the common factor of $- 14$ and $- 12$ .

Factor $- 2$ out of $- 14$ .

$x = \frac{- 2 (7)}{- 12}$

Cancel the common factors.

Factor $- 2$ out of $- 12$ .

$x = \frac{- 2 \cdot 7}{- 2 \cdot 6}$

Cancel the common factor.

$x = \frac{- 2 \cdot 7}{- 2 \cdot 6}$

Rewrite the expression.

$x = \frac{7}{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{6}$

Decimal Form:

$x = 1.1\overline{6}$

Mixed Number Form:

$x = 1 \frac{1}{6}$