Matematika

Pertanyaan

a.|x-3|=8
b.|x - 4 | < 3
c.|x - 3 | _> |2- x | harus dgan bukti. Thx.

1 Jawaban

  • A. |x - 3| = 8
    (x - 3)² - 8² = 0
    (x - 3 - 8)(x - 3 + 8) = 0
    (x - 11)(x + 5) = 0
    x = 11 atau x = - 5

    B. |x - 4| < 3
    (x - 4)² - 3² < 0
    (x - 4 + 3)(x - 4 - 3) < 0
    (x - 1)(x - 7) < 0
    1 < x < 7 

    C. |x - 3| ≥ |2 - x|
    (x - 3)² - (2 - x)² ≥ 0
    (x - 3 - (2 - x))(x - 3 + 2 - x) ≥ 0
    (2x - 1)(-1) ≥ 0
    - 2x + 1 ≥ 0 
    2x ≤ 1
    x ≤ 1/2

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