Nilai x yang memenuhi pertidaksamaan -1 < 2/3(2x-1)<_1 adalah......

Bab Pertidaksamaan
Matematika SMA Kelas X

-1 < (2/3) (2x - 1) ≤ 1

-1 = (2/3) (2x - 1)
-1 = (4x - 2)/3
-1 - (4x - 2)/3 = 0
(-3 - 4x + 2)/3 = 0
(-4x - 1)/3 = 0
-4x - 1 = 0
-4x = 1
x = -1/4

(2/3) (2x - 1) = 1
(4x - 2)/3 - 1 = 0
(4x -2 - 3)/3 = 0
(4x - 5)/3 = 0
4x - 5 = 0
4x = 5
x = 5/4

HP = { x | -1/4 < x ≤ 5/4, x ≠ 1/2, x ∈ bilangan real }

Materi : Matematika
Kelas : VIII SMP
Bab : Pertidaksamaan

Pembahasan :
-1 < 2/3(2x - 1) ≤ 1

Pecah Menjadi dua, yaitu :
2/3(2x - 1) ≤ 1
2(2x - 1) ≤ 3
4x - 2 ≤ 3
4x ≤ 5
x ≤ 5/4

2/3(2x - 1) > -1
2(2x - 1) > -3
4x - 2 > -3
4x > -1
x > -1/4

Hp : {-1/4 < x ≤ 5/4}