2|4x-3|-5|x+1|+|7-x|=0
=> 2|4-3x|+|7-x|=5|x+1|
Ta có bảng xét dấu:
x -1 3/4 7
2|4x-3| - | - 0 + | +
|7-x| + | + | + 0 +
5|x+1| - 0 + | + | +
_Nếu x < -1 thì:
-8x + 6 + 7 - x = -5x - 5
-8x - x + 5x = -5-6-7
-4x =-18
x =9/2 (loại)
_Nếu 1$\leq$ x < 3/4 - thì:
-8x + 6 +7 - x =5x +5
-8x -x -5x = 5-6-7
-14x =-8
x = 4/7 (T/m)
_Nếu 3/4 $\leq$ x < 7 thì:
8x - 6 + 7 - x = 5x + 5
8x - x - 5x =5 + 6 - 7
2x =4
x =2 (T/m)
_Nếu x $\leq$ 7 thì:
8x - 6 - 7 + x = 5x + 5
8x +x - 5x = 5+6+7
4x =18
x = 9/2 (T/m)
Vậy x∈{4/7; 2 ; 9/2}
