Đáp án `: a) x in { 19/30 ; 1/30 }`

`b)  x in { 3/2 ; -1/2 }`

`c) x in { 5/6 ; -1/6 }`

`d) x in { -1/8 ; -5/8 }`

Giải thích các bước giải:

`a) | x - 1/3 | = 1/2 - 1/5`

`=> | x - 1/3 | = 3/10`

`=>` $\left[\begin{matrix} x-\dfrac{1}{3}=\dfrac{3}{10}\\ x-\dfrac{1}{3}=\dfrac{-3}{10}\end{matrix}\right.$

`=>` $\left[\begin{matrix} x=\dfrac{3}{10}+\dfrac{1}{3}\\ x=\dfrac{-3}{10}+\dfrac{1}{3}\end{matrix}\right.$

`=>` $\left[\begin{matrix} x=\dfrac{19}{30}\\ x=\dfrac{1}{30}\end{matrix}\right.$

Vậy `x in { 19/30 ; 1/30 }`

`b) | 2x - 1 | + 4 = 6`

`=> | 2x - 1 | = 6 - 4`

`=> | 2x - 1 | = 2`

`=>` $\left[\begin{matrix} 2x-1=2\\ 2x-1=-2\end{matrix}\right.$

`=>` $\left[\begin{matrix} 2x=2+1\\ 2x=-2+1\end{matrix}\right.$

`=>` $\left[\begin{matrix} 2x=3\\ 2x=-1\end{matrix}\right.$

`=>` $\left[\begin{matrix} x=3:2\\ x=-1:2\end{matrix}\right.$

`=>` $\left[\begin{matrix} x=\dfrac{3}{2}\\ x=\dfrac{-1}{2}\end{matrix}\right.$

Vậy `x in { 3/2 ; -1/2 }`

`c) | x - 1/3 | = 1/2`

`=>` $\left[\begin{matrix} x-\dfrac{1}{3}=\dfrac{1}{2}\\ x-\dfrac{1}{3}=\dfrac{-1}{3}\end{matrix}\right.$

`=>` $\left[\begin{matrix} x=\dfrac{1}{2}+\dfrac{1}{3}\\ x=\dfrac{-1}{2}+\dfrac{1}{3}\end{matrix}\right.$

`=>` $\left[\begin{matrix} x=\dfrac{5}{6}\\ x=\dfrac{-1}{6}\end{matrix}\right.$

Vậy `x in { 5/6 ; -1/6 }`

`d) | 3/4 + 2x | - 1/2 = 0`

`=> | 3/4 + 2x | = 1/2`

`=>` $\left[\begin{matrix} \dfrac{3}{4}+2x=\dfrac{1}{2}\\ \dfrac{3}{4}+2x=\dfrac{-1}{2}\end{matrix}\right.$

`=>` $\left[\begin{matrix} 2x=\dfrac{1}{2}- \dfrac{3}{4}\\ 2x=\dfrac{-1}{2}- \dfrac{3}{4}\end{matrix}\right.$

`=>` $\left[\begin{matrix} 2x= \dfrac{-1}{4}\\ 2x=\dfrac{-5}{4}\end{matrix}\right.$

`=>` $\left[\begin{matrix} x= \dfrac{-1}{4}:2\\ x=\dfrac{-5}{4}:2\end{matrix}\right.$

`=>` $\left[\begin{matrix} x= \dfrac{-1}{8}\\ x=\dfrac{-5}{8}\end{matrix}\right.$

Vậy `x in { -1/8 ; -5/8 }`

Đáp án `+` Giải thích các bước giải:

`b)|2x-1|+4=6`

`=>|2x-1|=6-4`

`=>|2x-1|=2`

`@TH1:2x-1=2`

`=>2x=2+1`

`=>2x=3`

`=>x=3:2`

`=>x=1,5`

`@TH2:2x-1=``-2`

`=>2x=``-2+1`

`=>2x=``-1`

`=>x=(-1):2`

`=>x=``-0,5`

`=>x=1,5` hoặc `x=``-0,5`

Vậy `x∈{1,5;-0,5}`

_________________________________

`c)|x-1/3|=1/2`

`@TH1:x-1/3=1/2`

`=>x=1/2+1/3`

`=>x=5/6`

`@TH2:x-1/3=``-1/2`

`=>x=``-1/2+1/3`

`=>x=``-1/6`

`=>x=5/6` hoặc `x=``-1/6`

Vậy `x∈{5/6;-1/6}`

_______________________________

`d)|3/4+2x|-1/2=0`

`=>|3/4+2x|=0+1/2`

`=>|3/4+2x|=1/2`

`@TH1:3/4+2x=1/2`

`=>2x=1/2-3/4`

`=>2x=``-1/4`

`=>x=``-1/4:2`

`=>x=``-1/8`

`@TH2:3/4+2x=``-1/2`

`=>2x=``-1/2-3/4``

`=>2x=``-5/4`

`=>x=``-5/4:2`

`=>x=``-5/8`

`=>x=``-1/8` hoặc `x=``-5/8`

Vậy `x∈{-1/8;-5/8}`

$@lingg$