Step by step
The question
Question: solve 4x³ = 500.
x³ means x times x times x.
We want just x.
1 Remove the 4
4x³ means 4 times x³.
We want just x³.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just x³ is left.
500 divided by 4 is 125.
Now we have x³ = 125.
2 Cube root of both sides
The cube root asks: which number, times itself three times, makes this?
The cubes: 1 times 1 times 1 is 1.
2 times 2 times 2 is 8.
3 times 3 times 3 is 27.
4 times 4 times 4 is 64.
5 times 5 times 5 is 125.
x is the cube root of 125.
5 times 5 times 5 is 125.
So x = 5.
Careful!
A cube has one answer, not two.
Minus 5, cubed, is minus 125.
Not like x² = 49.
3 Check
Let's check: 5 times 5 times 5 is 125.
4 times 125 is 500.
The same as the right side.
So the answer is right!
Let's look back.
First: remove the 4.
Then: cube root of both sides.
Last: check.