Đề bài
Tìm x, biết :
\[\eqalign{ & a]\left[ {x - {5 \over {12}}} \right].{9 \over {29}} = - {6 \over {29}} \cr & b]0,5.x - {2 \over 3}.x = {7 \over {12}} \cr & c]5,2.x + 7{2 \over 5} = 6{3 \over 4} \cr & d]\left[ {{3 \over 7}x + 1} \right]:\left[ { - 4} \right] = {{ - 1} \over {28}}. \cr} \]
Lời giải chi tiết
\[\eqalign{ & a]\left[ {x - {5 \over {12}}} \right].{9 \over {29}} = - {6 \over {29}} \cr & x - {5 \over {12}} = {{ - 6} \over {29}}:{9 \over {29}} \cr & x - {5 \over {12}} = {{ - 6} \over {29}}.{{29} \over 9} \cr & x - {5 \over {12}} = {{ - 2} \over 3} \cr & x = {{ - 2} \over 3} + {5 \over {12}} \cr & x = {{ - 8} \over {12}} + {5 \over {12}} \cr & x = {{ - 3} \over {12}} \Leftrightarrow x = - {1 \over 4}. \cr & b]0,5x - {2 \over 3}x = {7 \over {12}} \Leftrightarrow {5 \over {10}}x - {2 \over 3}x = {7 \over {12}} \cr & \left[ {{5 \over {10}} - {2 \over 3}} \right].x = {7 \over {12}} \cr & \left[ {{1 \over 2} - {2 \over 3}} \right].x = {7 \over {12}} \cr & \left[ {{3 \over 6} - {4 \over 6}} \right].x = {7 \over {12}} \cr & - {1 \over 6}.x = {7 \over {12}} \cr & x = {7 \over {12}}:{{ - 1} \over 6} \Leftrightarrow x = {7 \over {12}}.[ - 6] \cr & x = - {7 \over 2} \Leftrightarrow x = - 3{1 \over 2}. \cr & c]5,2x + 7{2 \over 5} = 6{3 \over 4} \Leftrightarrow {{52} \over {10}}x + {{37} \over 5} = {{27} \over 4} \cr & {{26} \over 5}x = {{27} \over 4} - {{37} \over 5} \cr & {{26} \over 5}x = {{135} \over {20}} - {{148} \over {20}} \cr & {{26} \over 5}x = {{ - 13} \over {20}} \cr & x = {{ - 13} \over {20}}:{{26} \over 5} \cr & x = {{ - 13} \over {20}}.{5 \over {26}} \Leftrightarrow x = - {1 \over 8}. \cr & d]\left[ {{3 \over 7}x + 1} \right]:[ - 4] = {{ - 1} \over {28}} \cr & {3 \over 7}x + 1 = {{ - 1} \over {28}}.[ - 4] \cr & {3 \over 7}x + 1 = {1 \over 7} \Leftrightarrow {3 \over 7}x = {1 \over 7} - 1 \cr & {3 \over 7}x = {1 \over 7} - {7 \over 7} \Leftrightarrow {3 \over 7}x = {{ - 6} \over 7} \cr & x = {{ - 6} \over 7}:{3 \over 7} \cr & x = {{ - 6} \over 7}.{7 \over 3} \Leftrightarrow x = - 2. \cr} \]