Question

\(4\times\left|\frac{1}{3}x+\frac{1}{2}\right|+\left|\frac{-2}{3}\right|=-\frac{1}{25}\)

Giúp mik nha

Answer 1

\(4.\left|\frac{1}{3}x+\frac{1}{2}\right|+\left|-\frac{2}{3}\right|=-\frac{1}{25}\)

\(\)\(\Leftrightarrow4.\left|\frac{1}{3}x+\frac{1}{2}\right|+\frac{2}{3}=-\frac{1}{25}\)

\(\Leftrightarrow4.\left|\frac{1}{3}x+\frac{1}{2}\right|=-\frac{1}{25}-\frac{2}{3}\)

\(\Leftrightarrow4.\left|\frac{1}{3}x+\frac{1}{2}\right|=-\frac{53}{75}\)

\(\Leftrightarrow\left|\frac{1}{3}x+\frac{1}{2}\right|=-\frac{53}{75}:4\)

\(\Leftrightarrow\left|\frac{1}{3}x+\frac{1}{2}\right|=-\frac{53}{300}\)

\(\Rightarrow\) Vô lí ( Do \(\left|x\right|\ge0\) )

Vậy không có \(x\) thỏa mãn yêu cầu đề bài.

Answer 2

\(4.\left|\frac{1}{3}x+\frac{1}{2}\right|+\left|-\frac{2}{3}\right|=-\frac{1}{25}\)

⇔ \(4.\left|\frac{1}{3}x+\frac{1}{2}\right|+\frac{2}{3}=-\frac{1}{25}\)

⇔ \(4.\left|\frac{1}{3}x+\frac{1}{2}\right|=\left(-\frac{1}{25}\right)-\frac{2}{3}\)

⇔ \(4.\left|\frac{1}{3}x+\frac{1}{2}\right|=-\frac{53}{75}\)

⇔ \(\left|\frac{1}{3}x+\frac{1}{2}\right|=\left(-\frac{53}{75}\right):4\)

⇔ \(\left|\frac{1}{3}x+\frac{1}{2}\right|=-\frac{53}{300}\)

Ta luôn có: \(\left|x\right|>0\forall x\)

⇔ \(\left|\frac{1}{3}x+\frac{1}{2}\right|>-\frac{53}{300}\)

=> \(\left|\frac{1}{3}x+\frac{1}{2}\right|\ne-\frac{53}{300}\)

Vậy không tồn tại giá trị nào của \(x\) thỏa mãn yêu cầu đề bài.

Chúc bạn học tốt!