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Question: How many solutions does |x-3| = 4 have?

The equation |x-3| = 4 has two solutions. This is because absolute value equations often have multiple solutions: the numbers that are a certain distance away from zero in either direction. To solve this equation, we need to set up two separate equations: one for the positive solution and one for the negative solution. (1) x - 3 = 4 which gives x = 7 (2) -(x - 3) = 4 which gives x = -1 So the two solutions are x = -1 and x = 7.

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