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If |x-3|=2, find x....

If `|x-3|=2`, find x.

Text Solution

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Enter `|x-3|` into `Y_(1)` and 2 into `Y_(2)`. As seen in the figure below, the points of intersection are at x = 5 and x = 1.

This is also easy to see algebraically. If `|x-3|=2`, then `x-3=2 or x-3=-2`. Solving these equoations yields the same solutions, 5 or 1. This equation also has a coordinate geometry solution: `|a-b|` is the distance between a and b. Thus `|x-3|=2` has the interpretation that x is 2 units from 3. Therefore, x must be 5 or 1 .
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