a

X<1/5

X<1

b

X>1

X<-5/3

c

X=-1

X=7/3

a/ \(|5x-3|< 2\)                        b/ \(|3x+1>4|\)                             c/ \(|4-x|+2x=3\)

\(\Leftrightarrow5x-3< 2\)                          \(\Leftrightarrow3x+1>4\)                            \(\Leftrightarrow4-x+2x=3\)

 \(\Leftrightarrow5x< 5\)                                  \(\Leftrightarrow3x>3\)                                      \(\Leftrightarrow x=-1\)

 \(\Leftrightarrow x< 1\)                                     \(\Leftrightarrow x>1\)

\(a,\left|5x-3\right|< 2\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}\left|5x-3\right|=1\\\left|5x-3\right|=0\end{cases}}\)

\(TH1:\)\(\)

\(\left|5x-3\right|=1\)

\(\Leftrightarrow\orbr{\begin{cases}5x-3=1\\5x-3=-1\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}5x=1+3\\5x=-1+3\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}5x=4\\5x=2\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{4}{5}\left(\text{loại}\right)\\x=\frac{2}{5}\left(\text{loại}\right)\end{cases}}\)

\(TH2:\)

\(\left|5x-3\right|=0\)

\(\Leftrightarrow5x-3=0\)

\(\Leftrightarrow5x=0+3\)

\(\Leftrightarrow5x=3\)

\(\Leftrightarrow x=\frac{3}{5}\left(\text{loại}\right)\)

\(\text{Vậy : không tồn tại x cần tìm.}\)

\(b,\left|3x+1\right|>4\)

\(\Leftrightarrow\orbr{\begin{cases}3x+1>4\\3x+1< -4\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}3x>4-1\\3x< -4-1\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}3x>3\\3x< -5\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x>3\div3\\x< -5\div3\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x>1\\x< \frac{-5}{3}\end{cases}}\)

\(\text{Vậy : }\)\(x>1\)\(\text{hoặc}\)\(x< \frac{-5}{3}\)

\(\)