Solve for x (4x+10)^(1/4)=(9+7x)^(1/4)

${(4 x + 10)}^{\frac{1}{4}} = {(9 + 7 x)}^{\frac{1}{4}}$

Step 1

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

$4 x + 10 = 9 + 7 x$

Step 2

Solve for $x$ .

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

Subtract $7 x$ from both sides of the equation.

$4 x + 10 - 7 x = 9$

Subtract $7 x$ from $4 x$ .

$- 3 x + 10 = 9$

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

Subtract $10$ from both sides of the equation.

$- 3 x = 9 - 10$

Subtract $10$ from $9$ .

$- 3 x = - 1$

Divide each term in $- 3 x = - 1$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 1$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 1}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 1}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 1}{- 3}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{1}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{3}$

Decimal Form:

$x = 0.\overline{3}$