The inequality |x-3| < 2|x| can be solved by interpreting it as a statement about distances on the real line. The solution involves squaring both sides, leading to the equation x^2 - 6x + 9 < 4x^2. This simplifies to (x-3)^2 < 4x^2, which can be analyzed for two cases: when x is greater than or equal to 3 and when x is less than 3. The method used in the textbook applies the principle that |a| < |b| is equivalent to a^2 < b^2.
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TheRedDevil18 said:Homework Statement
Solve the given inequality by interpreting it as a statement about distances in the real line:
|x-3| < 2|x|
Homework Equations
The Attempt at a Solution
I have no clue what to do here and I do not understand the answer in the textbook
Goes something like this.....
x^2 - 6x + 9.....Have no idea how they got that
= (x-3)^2
...and so forth