Question

Nilai x yg memenuhi | x - 3 | > | 2x - 1| tolong plis . dg cara

Answer 1

Verified answer

Jawab

|x - 3| > |2x -1|

(i)
x - 3 >  -(2x -  1)
x - 3 > - 2x  + 1
x + 2x > 1 + 3
3x > 4
x > 4/3 (tm)

(ii)
x- 3 > 2x - 1
x - 2x  >  1 + 3
-x > 4
x  < - 4 (tm)

(iii)
-(x - 3) > 2x - 1
-x + 3 > 2x - 1
-x - 2x > -1 - 3
-3x > -4
x < 4/3 (m)

(iv)
-(x - 3) > -(2x - 1)
-x + 3 > -2x + 1
-x + 2x > 1 - 3
x > - 2 (m)

HP - 2 < x < 4/3

Answer 2

Verified answer

NiLai MutLak
• Pertidaksamaan

a² - b² = (a + b)(a - b)

•••
|x - 3| > |2x - 1|
(x - 3)² > (2x - 1)²
(x - 3)² - (2x - 1)² > 0 ---> perhatikan rumus diatas
((x - 3) + (2x - 1))((x - 3) - (2x - 1)) > 0
(3x - 4)(-x - 2) > 0

Pembuat nol
3x - 4 = 0 ---> x = 4/3
-x - 2 = 0 ---> x = -2

Uji titik
...- - -...(-2)...+++...(4/3)...- - -...

NiLai x yg memenuhi :
ambil daerah yg > 0 (+++)
-2 < x < 4/3