`a)`
`|x - 1| = 2`
`⇒` \(\left[ \begin{array}{l}x - 1 = 2\\x - 1 = -2\end{array} \right.\)
`⇒` \(\left[ \begin{array}{l}x = 3\\x = -1\end{array} \right.\)
`Vậy x = {3;1}`
`b)`
`|2x - 1| + 1 = 4`
`⇒ |2x - 1| = 3`
`⇒` \(\left[ \begin{array}{l}2x - 1 = 3\\2x - 1 = -3\end{array} \right.\)
`⇒` \(\left[ \begin{array}{l}x = 2\\x = -1\end{array} \right.\)
`Vậy x = {2 ; -1}`
`c)`
`8 - |1 - 3x| = 3`
`⇒ |1 - 3x| = 5`
`⇒` \(\left[ \begin{array}{l}1 - 3x = 5\\1 - 3x = -5\end{array} \right.\)
`⇒` \(\left[ \begin{array}{l}x = -4/3\\x = 2\end{array} \right.\)
`Vậy x = {-4/3 ; 2}`
`d)`
`|x - 1| + |x - 3| = 6`
`Với x - 1 ≥ 0 ; x - 3 ≥ 0`
`⇒ x ≥ 3`
`⇒ x - 1 + x - 3 = 6`
`⇒ 2x = 10`
`⇒ x = 5 (tm)`
`Với x - 1 < 0 ; x - 3 < 0`
`⇒ x < 1`
`⇒ 1 - x + 3 - x = 6`
`⇒ -2x = 2`
`⇒ x = -1 (tm)`
`Với x - 1 ≥ 0 ; x - 3 < 0`
`⇒ 1 ≤ x < 3`
`⇒ x - 1 + 3 - x = 6`
`⇒ 2 = 6 (vô lí)`
`Với x - 1 < 0 ; x - 3 ≥ 0`
`⇒ x ≥ 3 ; x < 1 (vô lí)`
`Vậy x = {5 ; -1}`
