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[Solved] Solving the absolute value equation

 
Basics of Algebra
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June 14, 2021 6:41 pm
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(@armor)
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Solve   |3x-|1-2x||=2.

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June 14, 2021 6:41 pm
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

\small |3x-|1-2x||=2\Rightarrow 3x-|1-2x|=\pm 2.

When  \small 3x-|1-2x|=2,    \small |1-2x|=3x-2,  then \small 3x-2\geq 0\Rightarrow x\geq 2/3  and  \small 1-2x=\pm (3x-2)  which leads to \small x=1   or \small x=3/5<2/3  (deleted).

When \small 3x-|1-2x|=-2,   \small |1-2x|=3x+2,  then \small 3x+2\geq 0\Rightarrow x\geq -2/3,  and \small 1-2x=\pm (3x+2) which leads to \small x=-1/5   or \small x=-3<-2/3  (deleted).

Hence, the original equation has solutions \small x=1   or  \small x=-1/5.

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