Question

|1-3a|= |a+2| doua module egale cum aflie a?

Answer 1

Explicitam modulele:

|1 - 3a| = 1 - 3a daca 1 - 3a ≥ 0 ⇒ a ≤ 1/3

|1 - 3a| = -(1 - 3a) daca 1 - 3a > 0 ⇒ a > 1/3

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|a + 2| = a + 2 daca a+2 ≥ 0 ⇒ a ≥ -2

|a + 2| = -(a + 2) daca a+2 < 0 ⇒ a < -2

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Daca a ∈ ( -∞, -2) avem ecuatia 1: 1 - 3a = -(a + 2)

Daca a ∈ [-2, 1/3) avem ecuatia 2: 1 - 3a = a + 2

Daca a ∈ [1/3, ∞) avem ecuatia 3: -(1 - 3a) = a + 2

Rezolvam ecuatiile:

1 - 3a = -(a + 2) pentru a ∈ ( -∞, -2)

1 - 3a = -a - 2

-3a + a = -2-1

-2a = -3

a = (-3)/(-2) = 3/2 = 1,5 (Solutie eliminata deoarece a > -2 )

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1 - 3a = a + 2 pentru a ∈ [-2, 1/3)

-3a - a = 2 - 1

-4a = 1

a = -1/4 = -,25

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-(1 - 3a) = a + 2 daca a ∈ [1/3, ∞)

-1+3a = a + 2

3a - a = 2 + 1

2a = 3

a = 3/2