Question

Matematika nilai mutlak

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

2) 2 < |2 - (x/2) | ≤ 3

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Answer 1

Verified answer

Kelas 10 Matematika
Bab Nilai Mutlak

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

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

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

{ 1, 3 }

2] 2 < |2 - (x/2)| ≤ 3

2 < |2 - (x/2)|
|2 - (x/2)| > 2

2 - (x/2) > 2
-(x/2) > 2 - 2
x < 0 . (-2)
x < 0

2 - (x/2) < -2
- (x/2) < -2 - 2
x > -4 . (-2)
x > 8 

x < 0 atau x > 8

|2 - (x/2)| ≤ 3
-3 ≤ 2 - (x/2) ≤ 3
-3 - 2 ≤ 2 - 2 - (x/2) ≤ 3 - 2
-5 ≤ (-x/2) ≤ 1
-5 . (-2) ≥ (-x/2) . (-2) ≥ 1 . (-2)
10 ≥ x ≥ -2
-2 ≤ x ≤ 10

Maka,
-2 ≤ x < 0 atau 8 < x ≤ 10