Question

|x-1| +2|2x-2|=9
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Answer 1

$Voi~folosi~urmatoarea~proprietate:~|a \cdot b|=|a| \cdot |b|. \\ \\ Deci~|2x-2|=|2(x-1)|=|2| \cdot |x-1|=2|x-1|. \\ \\ Deci~|x-1|+2 \cdot 2|x-1|=9. \\ \\ |x-1|+4|x-1|=9 \\ \\ 5|x-1|=9 \\ \\ |x-1|= \frac{9}{5} \Rightarrow x-1 = \pm \frac{9}{5} . \\ \\ x-1= \frac{9}{5} \Rightarrow x= \frac{9}{5}+1= \frac{14}{5}.$

$x-1=- \frac{9}{5} \Rightarrow x=- \frac{9}{5}+1= -\frac{4}{5}. \\ \\ \underline{Solutie}: x \in \Big\{- \frac{4}{5}; \frac{14}{5} \Big\}.$