- #26

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And since [tex]\sqrt{9}=3[/tex], the clearest way to write this is [tex]|x|=3[/tex], as Statdad said. Maybe going right to [tex]x=\pm 3[/tex] from [tex]x^2=9[/tex] is confusing you because it makes it seem like something is happening with the signs on the right side, when the right side is straightforward.

By the way, this is a very good question. You'll find that high school math glosses over many key points either to save time or avoid opening up a can of worms.