a)\(\left|x-1\right|+3x=1\)
\(\Rightarrow\left|x-1\right|=1-3x\)
\(\Rightarrow\orbr{\begin{cases}x-1=1-3x\\x-1=1+3x\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x+\left(-1\right)=1+\left(-3x\right)\\x+\left(-1\right)=1+3x\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x-\left(-3x\right)=1-\left(-1\right)\\x-3x=1-\left(-1\right)\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}4x=2\\-2x=2\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{1}{2}\\x=-1\end{cases}}\)
A ) | x - 1 | + 3x = 1
x - 1 + 3x = 1
( x + 3x ) - 1 = 1
4x - 1 = 1
4x = 1 + 1
4x = 2
x = 2 : 4
x = 0,5
Vậy x = 0,5
B) | 5x - 3 | - x = 7
5x - 3 - x = 7
( 5x - x ) - 3 = 7
4x - 3 = 7
4x = 7 + 3
4x = 10
x = 10 : 4
x = 2,5
Vậy x = 2,5
b)\(\left|5x-3\right|-x=7\)
\(\Rightarrow\left|5x-2\right|=7+x\)
\(\Rightarrow\orbr{\begin{cases}5x-2=7-x\\5x-2=7+x\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}5x+\left(-2\right)=7+\left(-x\right)\\5x+\left(-2\right)=7+x\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}5x-\left(-x\right)=7-\left(-2\right)\\5x-x=7-\left(-2\right)\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}6x=9\\4x=9\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=\frac{3}{2}\\x=\frac{9}{4}\end{cases}}\)