Question

2- Resolva: a) |x + 3| = 6 * 5 pontos {-3 ; 9} {3 ; 9} {3 ; -9} b) |2x – 6| = x + 2 * 5 pontos {8 ; -4/3} {8 ; 4/3} {-8 ; 4/3} c) |2x – 1| = |-x + 5| * 5 pontos {2 ; -4} {-2 ; -4} {2 ; 4} d) |x² – x – 4| = 2 * 5 pontos {-2 ; -3} {-2 ; 3} {2 ; -3} e) | x+3 | = 7 * 5 pontos {-4 ; -10} {-4 ; 10} {4 ; -10} f) |3x-8 | = 13 * 5 pontos {7 ; -5/3} {-7 ; 5/3} {7 ; 5/3}

Answer 1

Explicação passo-a-passo:

a)

|x + 3| = 6

• x + 3 = 6

x = 6 - 3

x = 3

• x + 3 = -6

x = -6 - 3

x = -9

S = {3, -9}

b)

|2x - 6| = x + 2

• 2x - 6 = x + 2

2x - x = 2 + 6

x = 8

• 2x - 6 = -x - 2

2x + x = -2 + 6

3x = 4

x = 4/3

S = {8, 4/3}

c)

|2x - 1| = |-x + 5|

• 2x - 1 = -x + 5

2x + x = 5 + 1

3x = 6

x = 6/3

x = 2

• 2x - 1 = x - 5

2x - x = -5 + 1

x = -4

S = {2, -4}

d)

|x² - x - 4| = 2

• x² - x - 4 = 2

x² - x - 4 - 2 = 0

x² - x - 6 = 0

Δ = (-1)² - 4.1.(-6)

Δ = 1 + 24

Δ = 25

x = (1 ± √25)/2.1 = (1 ± 5)/2

• x' = (1 + 5)/2 = 6/2 = 3

• x" = (1 - 5)/2 = -4/2 = -2

S = {-2, 3}

e)

|x + 3| = 7

• x + 3 = 7

x = 7 - 3

x = 4

• x + 3 = -7

x = -7 - 3

x = -10

S = {4, -10}

f)

|3x - 8| = 13

• 3x - 8 = 13

3x = 13 + 8

3x = 21

x = 21/3

x = 7

• 3x - 8 = -13

3x = -13 + 8

3x = -5

x = -5/3

S = {7, -5/3}