Question

|2x+1/3|=1 plsss ajutati-ma

Answer 1

a) 2x + 1/3 = -1, 2x = -1 - 1/3, 2x = -4/3, x = -2/3

b) 2x + 1/3 = 1, 2x = 1 - 1/3, 2x = 2/3, x = 1/3

Answer 2

$\it \Big{|}^{3)}2x+\dfrac{1}{3} \Big{|}=1 \Rightarrow\Big{|}\dfrac{6x+1}{3} \Big{|}=1 \Rightarrow \dfrac{|6x+1|}{|3|}=1\Rightarrow \dfrac{|6x+1|}{3}=1 \Rightarrow\\ \\ \Rightarrow|6x+1|=3 \Rightarrow 6x+1=\pm3 \Rightarrow 6x+1\in\{-3,3\}|_{-1}\Rightarrow6x\in\{-4,2\}|_{:2}\Rightarrow\\ \\ \\ \Rightarrow 3x\in \{-2,1\}|_{:3} \Rightarrow x\in\left\{-\dfrac{2}{3},\dfrac{1}{3}\right\}$

Mulțimea soluțiilor ecuației date este:

$\it S=\left\{-\dfrac{2}{3},\dfrac{1}{3}\right\}$