The goal in this equation is the get the x by itself. So, you need to take the cube root of both sides to eliminate the cube on the left side of your equation. After you have done that, you are left with x-1=2. You then add 1 to both sides of the equation in order to get x alone and you end up with x=3.

Given equation (x-1)^3=8

take cube root of both side

we get: (x - 1) = 2

or add 1 both side

x - 1 + 1 = 2 +1

x = 3

then answer is x = 3

Following the procedure underneath we can calculate the value of x.

We are given the equation

(x-1)^3 = 8 and

8 is cube of 2.

hence,

We have the equation:

(x-1)^3 = 8

We know that both sides of this equation are actually cubes. So, we can simplify this equation by cube-rooting both sides of this equation:

cube root of [(x-1)^3] = cube root of 8

On the left side, the cube root cancels out the ^3. So, we get x-1 on the left side. On the right side, the cube root of 8 is 2:

x - 1 = 2

Now, all we have to do is move the - 1 to the right side using inverse operations:

x - 1 **+ 1** = 2 **+ 1**

x = 3

Therefore, x = 3.