nilai x dari |x-7| = |3x-1|

Materi : Persamaan Mutlak

Pembahasan :
|x - 7| = |3x - 1|
(3x - 1)² = (x - 7)²
(3x - 1)² - (x - 7)² = 0
(3x - 1 + x - 7)(3x - 1 - x + 7) = 0
(4x - 8)(2x + 6) = 0
x = 2
x = -3

Hp : {-3 , 2}

| x - 7 | = | 3x - 1 |
( √( x - 7 )² )² = ( √(3x - 1)² )²
( x - 7 )² = ( 3x - 1 )²
( x - 7 )² - ( 3x - 1 )² = 0
( x - 7 + 3x - 1 ) ( x - 7 -( 3x - 1 ) ) = 0
( 4x - 8 ) ( x - 7 - 3x + 1 ) = 0
( 4x - 8 ) ( -2x - 6 ) = 0

4x - 8 = 0
4x = 8
x = 2

-2x - 6 = 0
-2x = 6
x = -3