Question

(1,0 điểm) Tìm $x$ biết

$\dfrac{2}{3} - |x-2,4|=\dfrac{1}{2}$.

Answer 1

\(\dfrac{2}{3}-\left|x-2,4\right|=\dfrac{1}{2}\)

\(\left|x-2,4\right|=\dfrac{2}{3}-\dfrac{1}{2}\)

\(\left|x-2,4\right|=\dfrac{1}{6}\)

*) Với \(x\ge2,4\) ta có:

\(x-2,4=\dfrac{1}{6}\)

\(x=\dfrac{1}{6}+2,4\)

\(x=\dfrac{77}{30}\) (nhận)

*) Với \(x< 2,4\) ta có:

\(x-2,4=-\dfrac{1}{6}\)

\(x=-\dfrac{1}{6}+2,4\)

\(x=\dfrac{67}{30}\) (nhận)

Vậy \(x=\dfrac{67}{30};x=\dfrac{77}{30}\)

Answer 2

   

\(\dfrac{2}{3}\)-|x-2,4|=\(\dfrac{1}{2}\)

     |x-2,4|=\(\dfrac{2}{3}\)-\(\dfrac{1}{2}\)

     |x-2,4|=\(\dfrac{1}{6}\) 

     x-2,4=\(\dfrac{1}{6}\) hoặc x-2,4=\(-\dfrac{1}{6}\)

     x       =\(\dfrac{1}{6}\)+2,4 hoặc x       = \(-\dfrac{1}{6}\)+2,4

     x         =\(\dfrac{77}{30}\)   hoặc  x        = \(\dfrac{67}{30}\)

Answer 3

\(\left|x-2,4\right|=\dfrac{2}{3}-\dfrac{1}{2}\\ \left|x-2,4\right|=\dfrac{1}{6}\\ \Rightarrow x-2,4=\dfrac{1}{6}\\ \Rightarrow x=\dfrac{1}{6}+2,4\\ x=\dfrac{77}{30}\)

hoặc

\(\Rightarrow x-2,4=-\dfrac{1}{6}\\ \Rightarrow x=-\dfrac{1}{6}+2,4\\ x=\dfrac{67}{30}\)

Answer 4

x = \(\dfrac{773}{300}\) hoặc x =\(\dfrac{673}{300}\)