Tentukan nilai x yang memenuhi persamaan |5×-10|=|5×+5|

Matematika Wajib
Persamaan Mutlak X SMA

Pembahasan :
Cara 1

|5x - 10| = |5x + 5|
(5x - 10)² = (5x + 5)²
(5x - 10)² - (5x + 5)² = 0
(10x - 5)(-15) = 0
-150x + 75 = 0
150x = 75
x = 1/2

Hp : {1/2}

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Cara 2

|5x - 10| = |5x + 5|

5x - 10 = 5x + 5
Tidak memenuhi

5x - 10 = -(5x + 5)
5x - 10 = -5x - 5
5x + 5x = -5 + 10
10x = 5
x = 1/2

Hp : {1/2}

|5x - 10| = |5x + 5|
(5x - 10)² = (5x + 5)²
25x² - 100x + 100 = 25x² + 50 + 25
-150x = -75
x = 1/2