How do I solve this equation? \sqrt[3]{x - 5} = \sqrt[3]{4x + 1}

Question

How do I solve this equation?

`\sqrt[3]{x - 5} = \sqrt[3]{4x + 1}`

Answer 1

Let's get rid of the cube roots. That will make the equations much easier to solve. To do this, we can cube both sides of the equation, as shown below:

`(\sqrt[3]{x - 5})^3 = (\sqrt[3]{4x + 1})^3`

`x - 5 = 4x + 1`

Now, we can easily solve the equation.

`-5 = 3x + 1`

`-6 = 3x`

`\boxed{x = -2}`

The equation has a solution of x = -2.

Answer 2

Hey there!!

∛x - 5 = ∛ 4x + 1

Cube on both sides

x - 5 = 4x + 1

Add 5 on both sides

... x = 4x + 6

Subtract 4x on both sides

... -3x = 6

Divide by -3 on both sides

... x = 6 / -3

... x = -2

Hence, the final answer is -2.

Hope my answer helps!!