`a) (x - 1)^2 = 1/4`

$\text { ⇒ \(\left[ \begin{array}{l}x - 1 = \frac{1}{2} \\x - 1 = \frac{-1}{2}\end{array} \right.\) }$

$\text { ⇒ \(\left[ \begin{array}{l}x = \frac{1}{2} + 1 \\x = \frac{-1}{2} + 1\end{array} \right.\) }$

$\text { ⇒ \(\left[ \begin{array}{l}x = \frac{1}{2} + \frac{2}{2} \\x = \frac{-1}{2} + \frac{2}{2}\end{array} \right.\) }$

$\text { ⇒ \(\left[ \begin{array}{l}x = \frac{3}{2} \\x = \frac{1}{2} \end{array} \right.\) }$

$\text { Vậy x ∈ { $\frac{3}{2}$ ; $\frac{1}{2}$ } }$

`b) 3/2 . x - 1 = x - 1/2`

`⇒ 3/2 . x - x = - 1/2 + 1`   (áp dụng quy tắc chuyển vế)

`⇒ ( 3/2 - 1) . x = - 1/2 + 2/2`

`⇒ ( 3/2 - 2/2 ) . x = 1/2`

`⇒  1/2 . x = 1/2`

`⇒  x = 1/2 : 1/2`

`⇒  x = 1`

$\text { Vậy x = 1 }$

`c) 5/6 - 3x = (-2)/3 + 1/2 . x`

`⇒ 5/6 + 2/3 = 1/2 . x + 3x`  (áp dụng quy tắc chuyển vế) 

`⇒ 5/6 + 4/6 = x . ( 1/2 + 3 )`

`⇒  9/6 = x . ( 1/2 + 6/2 )`

`⇒  9/6 = x . 7/2`

`⇒  x = 9/6 : 7/2`

`⇒  x = 9/6 . 2/7`

`⇒  x = 3/7`

$\text { Vậy x = $\frac{3}{7}$ }$

1, (x - 1)² = $\frac{1}{4}$

(x - 1)² = $\frac{1}{2}$²

⇒ \(\left[ \begin{array}{l}x-1=\frac{1}{2}\\x-1=\frac{-1}{2} \end{array} \right.\) 

⇒ \(\left[ \begin{array}{l}x=\frac{1}{2}+1\\x=\frac{-1}{2}+1\end{array} \right.\) 

⇒ \(\left[ \begin{array}{l}x=\frac{1+2}{2}=\frac{3}{2}\\x=\frac{-1+2}{2}=\frac{1}{2}\end{array} \right.\) 

2, $\frac{3}{2}$ x - 1 = x - $\frac{1}{2}$

$\frac{3}{2}$ x - x = $\frac{-1}{2}$ + 1

($\frac{3}{2}$ - 1) x = $\frac{-1+2}{2}$

($\frac{3-2}{2}$) x = $\frac{1}{2}$

$\frac{1}{2}$ x = $\frac{1}{2}$

x = $\frac{1}{2}$ : $\frac{1}{2}$

x = 1

3, $\frac{5}{6}$ - 3x = $\frac{-2}{3}$ + $\frac{1}{2}$ x

-3x - $\frac{1}{2}$ x = $\frac{-2}{3}$ - $\frac{5}{6}$

(-3 - $\frac{1}{2}$) x = $\frac{-4-5}{6}$

($\frac{-6-1}{2}$) x = $\frac{-9}{6}$

$\frac{-7}{2}$ x = $\frac{-9}{6}$ 

x = $\frac{-9}{6}$ : $\frac{-7}{2}$

x =  $\frac{-9}{6}$ . $\frac{-2}{7}$

x = $\frac{3}{7}$

Chúc bạn học tốt ^^