How do you solve x3 equals 4x?

Answer 1

Restate the question. Solve: x3 = 4x

(Algebra can be hard to write with a keyboard.)

x3 = 4x

x3/x = 4x/x {divide both sides by x}

x2 = 4*

x = plus or minus radical 2

x = +/- 2

*or you could go:

x2 - 4 = 0

(x - 2)(x+2) = 0

x - 2 = 0 or x + 2 = 0

x = 2 or x = -2

x = +/-2

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Answer 1:

3x = 4x

If you divide both sides by x, you get

3 = 4

So this approach doesn't seem to work. However, if you take all terms to the left side, you get:

3x - 4x = 0

-x = 0

Multiplying by (-1):

x = 0

So zero is the solution. The reason the first approach didn't work is because I was dividing by zero. If you do try this - and it makes sense, for more complicated equations - you have to separately analyze the possibility that x = 0.