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|a|-|b|<=|a-b| You know that |a-b| means the distance between a and b on the number line. So, you’ve got two points on the number line, a and b . Picture folding the number line in 1/2 to put the negative side on top of the positive side. So, what happened? Well, if both a and b were the same sign, their distances didn’t change. If a and b had opposite signs they just got closer. Well, when we folded, a went to |a| and b went to |b| . So, now we know that the distance between |a| and |b| might be the same as the distance between a and b or it could be less. So, |a|−|b|≤|a−b|