Question

Giá trị x < 0 thỏa mãn :

\(\left|2x-\dfrac{1}{2}\right|+\dfrac{3}{7}=5\dfrac{3}{7}\)

 

Answer 1

\(\left|2x-\frac{1}{2}\right|+\frac{3}{7}=5\frac{3}{7}\)

\(\left|2x-\frac{1}{2}\right|=\frac{38}{7}-\frac{3}{7}\)

\(\left|2x-\frac{1}{2}\right|=5\)

Ta xét hai trường hợp:

TH1: \(2x-\frac{1}{2}=5\)

2x = 5 + 1/2

2x = 11/2

x = 11/2 : 2

x = 11/4 (loại vì x < 0)

TH2: 2x - 1/2 = -5

2x = -5 + 1/2

2x = -9/2

x = -9/2:2

x = -9/4 (chọn)

Vậy x = -9/4

Answer 2

\(\left|2x-\frac{1}{2}\right|+\frac{3}{7}=5\frac{3}{7}\)

\(\left|2x-\frac{1}{2}\right|=5\frac{3}{7}-\frac{3}{7}=5\)

\(\Rightarrow\orbr{\begin{cases}2x-\frac{1}{2}=5\\2x-\frac{1}{2}=-5\end{cases}}\Rightarrow\orbr{\begin{cases}2x=\frac{11}{2}\\2x=\frac{-9}{2}\end{cases}\Rightarrow\orbr{\begin{cases}x=11\\x=-9\end{cases}}}\)

\(x=-9\)