When solving this equation, how can we cancel x^2 and x? (this is the only way we arrive to the answer shown) The answer would be true only if x>0 but that is not stated in the question. The answer would vary if x<0 and we cannot cancel variables in an equation.

Feel free to correct me, thanks!

Can you provide the answer where x<0?

For x/100 = 4x^2, you can divide both sides by x without making any assumptions about x, OTHER than x is not equal to 0 (which is stated in the prompt).

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But we cannot divide both sides by x because we cannot cancel variables with different powers

We can divide both sides of an equation by any number that is not zero, and the equation remains valid. Therefore, we can definitely divide both sides of an equation by x, as long as x is not equal to zero.

Iâ€™m not sure what you mean by â€ścancelling variablesâ€ť, but I think your application of that rule does not apply in this scenario.