Phương pháp giải:

Sử dụng quy tắc cộng trừ hai số nguyên khác dấu và \(\left| a \right| = \left\{ \matrix{a(a \ge 0)\cr - a(a < 0)  \cr}  \right.\) để tìm x

Lời giải chi tiết:

\(\eqalign{ & a)\,\,\,x - 1 =  - 9  \cr & \,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\, =  - 9 + 1  \cr & \,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\, =  - (9 - 1)  \cr & \,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\, =  - 8. \cr} \)    

Vậy  \(x=-8.\)  

\(\begin{array}{l}b)\,\,\,\left| {x - 2} \right| + 7 = 12\\\,\,\,\,\,\,\,\,\left| {x - 2} \right|\,\,\,\,\,\,\,\,\,\, = 12 - 7\\\,\,\,\,\,\,\,\,\left| {x - 2} \right|\,\,\,\,\,\,\,\,\,\, = 5.\end{array}\)

\(\begin{array}{l}TH1:x - 2 = 5\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\,\, = 5 + 2\\\,\,\,\,\,\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\,\, = 7.\end{array}\) 

\(\begin{array}{l}TH2:\,\,x - 2 = - 5\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\,\, = - 5 + 2\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\,\, = - (5 - 2)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\,\,\,\,\,\,\,\,\,\, = - 3.\end{array}\)

Vậy \(x=7\) hoặc \(x=-3.\)