Question

Solutile ecuatiei |x-$\frac{2}{3}$|=$2 \frac{1}{2}$

Answer 1

2*1/2 = 5/2

x - 2/3 = 5/2                    x - 2/3 = - 5/2
x = 5/2 + 2/3                   x = - 5/2 + 2/3 
x= 15/6+4/6                     x = - 15/6 + 4/6 
x = 19/6                            x = - 11/6

Answer 2

$\Big|x-\dfrac{2}{3}\Big| = 2\dfrac{1}{2} \\ \\ \Big|x-\dfrac{2}{3}\Big| = \dfrac{2\cdot 2+1}{2} \\ \\ \Big|x-\dfrac{2}{3}\Big| = \dfrac{4+1}{2} \\ \\ \Big|x-\dfrac{2}{3}\Big| = \dfrac{5}{2}\\ \\ x-\dfrac{2}{3} = \pm \dfrac{5}{2}$

$\boxed{1}\quad x-\dfrac{2}{3} = +\dfrac{5}{2} \Rightarrow x = ^{\Big{3)}}\dfrac{5}{2}+^{\Big{2)}}\dfrac{2}{3} \Rightarrow x = \dfrac{15+4}{6} \Rightarrow \boxed{x = \dfrac{19}{6}} \\ \\ \boxed{2} \quad x-\dfrac{2}{3} = -\dfrac{5}{2} \Rightarrow x = -\dfrac{5}{2}+\dfrac{2}{3} \Rightarrow x = ^{\Big{2)}}\dfrac{2}{3}-^{\Big{3)}}\dfrac{5}{2} \Rightarrow x=\dfrac{4-15}{6}\Rightarrow \\ \\ \Rightarrow \boxed{x =- \dfrac{11}{6}}$

$\\ \\ Din \boxed{1} \cup \boxed{2} \Rightarrow \boxed{S = \Big\{-\dfrac{11}{6},\dfrac{19}{6}\Big\}}$