a)|-2x + 1,5| = 1/4
=>(-2x + 1,5) ∈ {1/4;-1/4}
TH1:-2x + 1,5 = 1/4 TH2:-2x + 1,5 = -1/4
-2x=1/4-1,5 -2x=-1/4-1,5
-2x=-5/4 -2x=-7/4
x=-5/4:(-2) x=-7/4:(-2)
x=5/8. x=7/8.
Vậy x ∈ {5/8 ; 7/8}
b)3/2 - | 5/4 +3x| = 1/4
| 5/4 +3x| = 3/2 - 1/4
| 5/4 +3x| = 5/4
=>(5/4 +3x) ∈ {5/4 ; -5/4}
TH1:5/4 +3x = 5/4 TH2:5/4 +3x = -5/4
3x= 5/4 - 5/4 3x= -5/4 - 5/4
3x= 0 3x= -5/2
x=0 : 3 x=-5/2 : 3
x=0. x= -5/6.
Vậy x ∈ {0 ; -5/6}
c)|4x -1| - | 3x - 1/2| = 0
<=>4x -1=3x - 1/2
<=>4x-3x=-1/2+1
<=>x=1/2
Vậy x=1/2
d) | x- 1| - 2x = 1/2
| x- 1| = 1/2 + 2x
=> (x - 1) ∈ { (1/2 +2x) ; -(1/2+2x) }
TH1: x - 1 = 1/2 +2x TH2: x - 1 = -(1/2 +2x )
-1-1/2 = 2x -x x - 1 = -1/2 -2x
x=-3/2. x + 2x = -1/2 + 1
3x = 1/2
x = 1/2 : 3
x = 1/6.
Vậy x ∈ {-3/2 ; 1/6}
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