Question

Completa la tabla con el respectivo valor de x (p.9):

Ecuación Valor de x

7x - 2/3 = 5x + 1/2
2/5x - 2/3 = x - 1/5
(x-3)/2 + (3x+1)/2 = 1
√(3)/2x - x = √(3)/2x + 2
2/x + 3/x = 1/2
2/x-1 + 2/x+2 = 1

Answer 1

Resolver
Hallar valor de X

7x - 2/3 = 5x + 1/2
2/5x - 2/3 = x - 1/5
(x-3)/2 + (3x+1)/2 = 1
√(3)/2x - x = √(3)/2x + 2
2/x + 3/x = 1/2
2/x-1 + 2/x+2 = 1

Solución
7x - 2/3 = 5x + 1/2
7x - 5x = 1/2 + 2/3
2x = (3 + 4)/6
2x = 7/6
x = 7/12

2/5x - 2/3 = x - 1/5
2/5x = x - 1/5 + 2/3
2 = 5x (x - 1/5 + 2/3)
2 = 5x² - x + 10x/3
5x² - x + 10x/3 - 2 = 0
(15x² - 3x + 10x )/3 = 0
15x² + 7x = 0
x₁ = -7/15
x₂ = 0

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

((√3)/2)x - x = (√(3)/2)x + 2
((√3)/2)x - (√(3)/2)x - x = 2
-x = 2
x = -2


2/x + 3/x = 1/2
(2 + 3)/x = 1/2
5 = x/2
x = 5/2 = 2,5

2/x-1 + 2/x+2 = 1
2/x-1 = 1 - 2/x+2
2 = (1 - 2/x+2) (x - 1)
2 = x - 2x/(x+2) - 1 + 2/x+2
3 = x - 2x/(x+2) + 2/(x+2)
(3x + 6)/(x+2) = (x² + 2x - 2x + 2)/(x+2) 
3x + 6 = x² + 2x - 2x + 2
0 = x² + 2 - 6 - 3x
x² - 3x - 4 = 0
x₁ = -1
x₂ = 4

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