algebra ejercicio 80 resueltos
Respuestas a la pregunta
Del libro de texto "Álgebra" del Profesor Aurelio Baldor se revuelven algunos de los problemas del ejercicio 80.
1) x + 3(x - 1) = 6 – 4(2x + 3)
x + 3x – 3 = 6 – 8x – 12
4x – 3 = - 8x – 6
12x = - 3
X = - 3/12
X = - 1/4
2) 5(x – 1) + 12(2x + 3) = 3(2x - 7)
5x – 5 + 32x + 48 = 6x – 21 – x
37x + 43 = 5x – 21
37x – 5x = - 21 – 43
32x = - 64
X = - 64/32
X = - 2
3) 2(3x + 3) – 4(5x - 3) = x(x – 3) – x(x + 5)
6x + 6 – 20x + 12 = x² – 3x – x² – 5x
-14x + 18 = - 8x
-14x + 8x = - 18
-6x = - 18
X = - 18/- 6
X = 3
4) 184 – 7(2x + 5) = 301 + 6(x – 1) – 6
184 – 14x – 35 = 301 + 6x – 6 – 6
149 – 14x = 289 + 6x
149 – 289 = 6x + 14x
-140 = 20x
X = - 140/20
X = - 7
5) 7(18 – x) – 6(3 – 5x) = - (7x + 9) – 3(2x + 5) - 12
126 – 7x – 18 + 30x = - 7x – 9 – 6x – 15 – 12
23x + 108 = – 13x – 36
23x + 13x = - 36 - 108
36x = - 144
X = - 144/36
X = 4
6) 3x(x – 3) + 5(x + 7) – x(x + 1) – 2(x2 + 7) + 4 = 0
3x² – 9x + 5x + 35 – x² – x – 2x² – 14 + 4 = 0
-5x + 25 = 0
-5x = - 25
X = - 25/ -5
X = 5
7) -3(2x + 7) + (- 5x + 6) – 8(1 – 2x) – (x – 3) = 0
-6x – 21 – 5x + 6 – 8 + 16x – x + 3 = 0
4x – 20 = 0
4x = 20
X = 20/4
X = 5
8) (3x – 4)(4x - 3) = (6x - 4)(2x – 5)
12x² – 9x – 16x + 12 = 12x² – 38x + 20
-25x + 38x = 20 – 12
13x = 8
X = 8/13
9) (4 – 5x )(4x - 5) = (10x - 3)(7 – 2x)
-20x² + 41x - 20 = - 20x² + 76x – 21
41x – 76x = - 21 + 20
-35x = - 1
X = - 1/- 35
X = 1/35
10) (x + 1)(2x + 5) = (2x + 3)(x - 4) + 5
2x² + 7x + 5 = 2x² – 5x – 12 + 5
7x + 5x = - 7 - 5
12x = - 12
X = - 12/12
X = - 1
11) (x – 2)² – (3 –x )² = 1
x² – 4x + 4 – 9 + 6x – x² = 1
2x – 5 = 1
2x = 6
X = 6/2
X = 3
El resto de los ejercicios se dejan par que el interesado los resuelva y fije de ese modo los conocimientos en el tema.
Respuesta:
1) x + 3(x - 1) = 6 – 4(2x + 3)
x + 3x – 3 = 6 – 8x – 12
4x – 3 = - 8x – 6
12x = - 3
X = - 3/12
X = - 1/4
2) 5(x – 1) + 12(2x + 3) = 3(2x - 7)
5x – 5 + 32x + 48 = 6x – 21 – x
37x + 43 = 5x – 21
37x – 5x = - 21 – 43
32x = - 64
X = - 64/32
X = - 2
3) 2(3x + 3) – 4(5x - 3) = x(x – 3) – x(x + 5)
6x + 6 – 20x + 12 = x² – 3x – x² – 5x
-14x + 18 = - 8x
-14x + 8x = - 18
-6x = - 18
X = - 18/- 6
X = 3
4) 184 – 7(2x + 5) = 301 + 6(x – 1) – 6
184 – 14x – 35 = 301 + 6x – 6 – 6
149 – 14x = 289 + 6x
149 – 289 = 6x + 14x
-140 = 20x
X = - 140/20
X = - 7
5) 7(18 – x) – 6(3 – 5x) = - (7x + 9) – 3(2x + 5) - 12
126 – 7x – 18 + 30x = - 7x – 9 – 6x – 15 – 12
23x + 108 = – 13x – 36
23x + 13x = - 36 - 108
36x = - 144
X = - 144/36
X = 4
6) 3x(x – 3) + 5(x + 7) – x(x + 1) – 2(x2 + 7) + 4 = 0
3x² – 9x + 5x + 35 – x² – x – 2x² – 14 + 4 = 0
-5x + 25 = 0
-5x = - 25
X = - 25/ -5
X = 5
7) -3(2x + 7) + (- 5x + 6) – 8(1 – 2x) – (x – 3) = 0
-6x – 21 – 5x + 6 – 8 + 16x – x + 3 = 0
4x – 20 = 0
4x = 20
X = 20/4
X = 5
8) (3x – 4)(4x - 3) = (6x - 4)(2x – 5)
12x² – 9x – 16x + 12 = 12x² – 38x + 20
-25x + 38x = 20 – 12
13x = 8
X = 8/13
9) (4 – 5x )(4x - 5) = (10x - 3)(7 – 2x)
-20x² + 41x - 20 = - 20x² + 76x – 21
41x – 76x = - 21 + 20
-35x = - 1
X = - 1/- 35
X = 1/35
10) (x + 1)(2x + 5) = (2x + 3)(x - 4) + 5
2x² + 7x + 5 = 2x² – 5x – 12 + 5
7x + 5x = - 7 - 5
12x = - 12
X = - 12/12
X = - 1
11) (x – 2)² – (3 –x )² = 1
x² – 4x + 4 – 9 + 6x – x² = 1
2x – 5 = 1
2x = 6
X = 6/2
X = 3
Explicación: