Are acid-fast bacteria Gram-positive or Gram-negative?

Both procedures involve using a stain, decolorising agent, and then a second stain. I am tempted to conclude that acid-fast bacteria, which resist decolorisation (eg. by strong carbol fuchsin), also resist decolorisation in the Gram staining test (eg. by gentian violet) and are thus Gram-positive.After all, there are much fewer acid-fast bacteria than Gram-positive bacteria.

Is this line of thinking incorrect?

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