1 +1 = 3, 3 voi 3 la 4, 4 voi 1 la ba, 3 ngon tay that deu
a. | x - 1/7 | + 3/7 = 0
<=> | x - 1/7 | = - 3/7
Mà \(\left|x-\frac{1}{7}\right|\ge0\forall x\)
=> Không có x tm đề bài
b. | x + 1/4 | - 3/4 = 5%
<=> | x + 1/4 | = 4/5
<=> \(\orbr{\begin{cases}x+\frac{1}{4}=\frac{4}{5}\\x+\frac{1}{4}=-\frac{4}{5}\end{cases}}\)<=> \(\orbr{\begin{cases}x=\frac{11}{20}\\x=-\frac{21}{20}\end{cases}}\)
c. | - x + 2/5 | + 1/2 = 3,5
<=> | - x + 2/5 | = 3
<=> \(\orbr{\begin{cases}-x+\frac{2}{5}=3\\-x+\frac{2}{5}=-3\end{cases}}\)<=>\(\orbr{\begin{cases}x=-\frac{13}{5}\\x=\frac{17}{5}\end{cases}}\)
a) \(\left|x-\frac{1}{7}\right|+\frac{3}{7}=0\)
\(\Leftrightarrow\left|x-\frac{1}{7}\right|=-\frac{3}{7}\)
=> vô lý
PT vô nghiệm
b) \(\left|x+\frac{1}{4}\right|-\frac{3}{4}=5\%\)
\(\Leftrightarrow\left|x+\frac{1}{4}\right|=\frac{4}{5}\)
\(\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{4}=\frac{4}{5}\\x+\frac{1}{4}=-\frac{4}{5}\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{11}{20}\\x=-\frac{21}{20}\end{cases}}\)
c) \(\left|-x+\frac{2}{5}\right|+\frac{1}{2}=3,5\)
\(\Leftrightarrow\left|\frac{2}{5}-x\right|=3\)
\(\Leftrightarrow\orbr{\begin{cases}\frac{2}{5}-x=3\\\frac{2}{5}-x=-3\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{13}{5}\\x=\frac{17}{5}\end{cases}}\)
Bài giải
a, \(\left|x-\frac{1}{7}\right|+\frac{3}{7}=0\)
\(\left|x-\frac{1}{7}\right|=-\frac{3}{7}\text{ }\left(\text{ Loại vì }\left|x-\frac{1}{7}\right|\ge0\forall x\right)\)
b, \(\left|x+\frac{1}{4}\right|-\frac{3}{4}=\frac{5}{100}=\frac{1}{20}\)
\(\left|x+\frac{1}{4}\right|=\frac{4}{5}\)
\(\Rightarrow\orbr{\begin{cases}x+\frac{1}{4}=-\frac{4}{5}\\x+\frac{1}{4}=\frac{4}{5}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{-21}{20}\\x=\frac{11}{20}\end{cases}}\)
c, \(\left|-x+\frac{2}{5}\right|+\frac{1}{2}=3,5=\frac{7}{2}\)
\(\left|-x+\frac{2}{5}\right|=3\)
\(\Rightarrow\orbr{\begin{cases}-x+\frac{2}{5}=-3\\-x+\frac{2}{5}=3\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{17}{5}\\x=-\frac{13}{5}\end{cases}}\)
