| x - 1 | + 7 = 3x

Lời giải của Luyện Tập 247

Giải chi tiết:

(begin{array}{l}left| {x - 1} right| + 7 = 3x\ Leftrightarrow left| {x - 1} right| = 3x - 7\ Leftrightarrow left[ begin{array}{l}left{ begin{array}{l}x - 1 ge 0\x - 1 = 3x - 7end{array} right.\left{ begin{array}{l}x - 1 < 0\ - left( {x - 1} right) = 3x - 7end{array} right.end{array} right. Leftrightarrow left[ begin{array}{l}left{ begin{array}{l}x ge 1\x - 1 = 3x - 7end{array} right.\left{ begin{array}{l}x < 1\ - x + 1 = 3x - 7end{array} right.end{array} right.\ Leftrightarrow left[ begin{array}{l}left{ begin{array}{l}x ge 1\3x - x =  - 1 + 7end{array} right.\left{ begin{array}{l}x < 1\x + 3x = 7 + 1end{array} right.end{array} right. Leftrightarrow left[ begin{array}{l}left{ begin{array}{l}x ge 1\2x = 6end{array} right.\left{ begin{array}{l}x < 1\4x = 8end{array} right.end{array} right. Leftrightarrow left[ begin{array}{l}left{ begin{array}{l}x ge 1\x = 3end{array} right.\left{ begin{array}{l}x < 1\x = 2end{array} right.end{array} right. Leftrightarrow x = 3.end{array})

Vậy phương trình có nghiệm duy nhất (x = 3.)

Chọn C.