|3x + \(\frac{1}{2}\) | + |3x + \(\frac{1}{6}\)| + |3x + \(\frac{1}{12}\)| + ... + |3x + \(\frac{1}{380}\)| = 58x
Vì |3x + \(\frac{1}{2}\) | + |3x + \(\frac{1}{6}\)| + |3x + \(\frac{1}{12}\)| + ... + |3x + \(\frac{1}{380}\)| ≥ 0
\(\Leftrightarrow\) 58x ≥ 0
\(\Leftrightarrow\) x ≥ 0
Khi đó:
|3x + \(\frac{1}{2}\) | + |3x + \(\frac{1}{6}\)| + |3x + \(\frac{1}{12}\)| + ... + |3x + \(\frac{1}{380}\)| =
(3x + \(\frac{1}{2}\)) + (3x + \(\frac{1}{6}\)) + ... + (3x + \(\frac{1}{380}\)) = 58x
\(\Leftrightarrow\) (3x + \(\frac{1}{1.2}\)) + (3x + \(\frac{1}{2.3}\)) + ... + (3x + \(\frac{1}{19.20}\)) = 58x
\(\Leftrightarrow\) (3x + 3x + ... + 3x) + (\(\frac{1}{1.2}\) + \(\frac{1}{2.3}\) + ... + \(\frac{1}{19.20}\)) = 58x
\(\Leftrightarrow\) 3x\(\left[\left(19-1\right):1+1\right]\) + (1 - \(\frac{1}{2}\) + \(\frac{1}{2}\) - \(\frac{1}{3}\) + ... + \(\frac{1}{19}\) - \(\frac{1}{20}\)) = 58x
\(\Leftrightarrow\) 57x + (1 - \(\frac{1}{20}\)) = 58x
\(\Leftrightarrow\) x = \(\frac{19}{20}\)
