tentukan nilai x yg memenuhi persamaan nilai mutlak berikut : a. |x-2|=3 b. |x-1| = |x+3| c. |x+3/x-2|=4 d. |x-3|<3 e. |x²-2x+1|-12<0 f . |x-3/x+2|<1 g. |x-2|²<

a. |x-2| = 3
|x-2| { x-2 , x-2 >_ 0 { x-2 , x >_ 5
{ -x+2 , x-2 < 0 { -x+2 , x < 5

untuk x>_ 5.
x-2 = 3
x = 3+2
x = 5
5>_ 5 (memenuhi)

untuk x< 5
-x+2 = 3
-x = 3-2
-x = 1
x = -1
-1 < 5 (memenuhi)

b.|x-1| = |x+3|
(x-1)² = (x-3)²
(x-1) ( x-1) = (x-3) (x-3)
x² - x - x + 1 = x² -3x -3x + 9
x² -2x +1 = x² -6x + 9
x² - x² -2x+6x +1-9 =0
4x -8 = 0
4x = 8
x = 8/4
x= 2

c. x+3
------ = 4
x-2

x+3 -4 = 0
---------
x - 2

x+3 - 4(x-2). = 0
-----------------
x- 2

x+3 - 4x+8
-------------- = 0
x-2

-3x + 11
----------. =0
x-2

-3x+11 =0
-3x = -11
x = -11/-3
x = 11/3

x-2 = 0
x = 2