Solve for x fourth root of 3x+3 = fourth root of 2x-7

$\sqrt[4]{3 x + 3} = \sqrt[4]{2 x - 7}$

Step 1

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $4$ .

${\sqrt[4]{3 x + 3}}^{4} = {\sqrt[4]{2 x - 7}}^{4}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{3 x + 3}$ as ${(3 x + 3)}^{\frac{1}{4}}$ .

${({(3 x + 3)}^{\frac{1}{4}})}^{4} = {\sqrt[4]{2 x - 7}}^{4}$

Simplify the left side.

Simplify ${({(3 x + 3)}^{\frac{1}{4}})}^{4}$ .

Multiply the exponents in ${({(3 x + 3)}^{\frac{1}{4}})}^{4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(3 x + 3)}^{\frac{1}{4} \cdot 4} = {\sqrt[4]{2 x - 7}}^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(3 x + 3)}^{\frac{1}{4} \cdot 4} = {\sqrt[4]{2 x - 7}}^{4}$

Rewrite the expression.

${(3 x + 3)}^{1} = {\sqrt[4]{2 x - 7}}^{4}$

Simplify.

$3 x + 3 = {\sqrt[4]{2 x - 7}}^{4}$

Simplify the right side.

Rewrite ${\sqrt[4]{2 x - 7}}^{4}$ as $2 x - 7$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{2 x - 7}$ as ${(2 x - 7)}^{\frac{1}{4}}$ .

$3 x + 3 = {({(2 x - 7)}^{\frac{1}{4}})}^{4}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3 x + 3 = {(2 x - 7)}^{\frac{1}{4} \cdot 4}$

Combine $\frac{1}{4}$ and $4$ .

$3 x + 3 = {(2 x - 7)}^{\frac{4}{4}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$3 x + 3 = {(2 x - 7)}^{\frac{4}{4}}$

Rewrite the expression.

$3 x + 3 = {(2 x - 7)}^{1}$

Simplify.

$3 x + 3 = 2 x - 7$

Step 3

Solve for $x$ .

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

Subtract $2 x$ from both sides of the equation.

$3 x + 3 - 2 x = - 7$

Subtract $2 x$ from $3 x$ .

$x + 3 = - 7$

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

Subtract $3$ from both sides of the equation.

$x = - 7 - 3$

Subtract $3$ from $- 7$ .

$x = - 10$

Step 4

Exclude the solutions that do not make $\sqrt[4]{3 x + 3} = \sqrt[4]{2 x - 7}$ true.

$No solution$

Solve for x fourth root of 3x+3 = fourth root of 2x-7

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