7. Nilai x yang memenuhi pertidaksamaan | x-1 | + | x-3 | = 2 adalah

Mapel : Matematika
Kelas : X SMA
Bab : Mutlak

Pembahasan :
|x - 1| + |x - 3| = 2

x - 1 + x - 3 = 2
2x - 4 = 2
2x = 6
x = 3

x - 1 + x - 3 = -2
2x - 4 = -2
2x = 2
x = 1

Hp : {1 , 3}

|x - 1| + |x - 3| = 2

|x - 1| = x - 1 ...(i) jk x >/= 1
|x - 1| = -x + 1 ...(ii) jk x < 1
|x - 3| = x - 3 ...(iii) jk x >/= 3
|x - 3| = -x + 3 ...(iv) jk x < 3

(I) x < 1
-x + 1 + (-x + 3) = 2
-2x + 4 = 2
-2x = -2
x = 1

(II) 1</= x < 3
x - 1 + (-x + 3) = 2
0x + 2 = 2
0x = 0

(III) x>/= 3
x - 1 + (x - 3) = 2
2x - 4 = 2
2x = 6
x = 3