Ecuaciones Lineales Ejemplos

Compruebe si el (los) número (s) dado (s) es (son) solución (es) de las ecuaciones correspondientes.
1. 3x + 7 = 12 – 2x ; 1
3x + 2x = 12-7
5x = 5
X = 5/5= 1

3. [(u+2)/(3u – 1)] + 1 = (6 –u)/(u + 1); 2

5. x2 = 5x – 6; 2,5
x2- 5x + 6 = 0
(x – 3) (x-2)

7. (5/x) – (3/2x) = x/2; 3

9. [3/(x- 1)] – [5x /(x + 2)] = 1/4; 1

Reduzca las ecuaciones siguientes a ecuacionespolinominales y declare el grado resultante

11. x3-7x2+ 5 = x(x2-1) + 3x2-2
x3-7x2+ 5 = x3- x + 3x2- 2
x3-7x2 – x3+ x – 3x2= -2 – 5
-10x2+ x= -7

13. y2+7 = (y – 1)2+ 3yy2+7 = y2-2 (y) (1) +12 + 3y
y2+7 = y2- 2y + 1 + 3y
y2 – y2+ 2y – 3y= 1 – 7
-y= -6

Resuelva las siguientes ecuaciones

15. 1 + x = 3 – x
x + x = 3 – 1
2x = 2
x =2/2
x = 1

17. 2x -5 = -15 – 3x
2x + 3x = -15 + 5
5x = -10
x = -10/5
x = -2

19. 4 (x - 3) = 8 – x
4x – 12 = 8 – x
4x + x = 8 + 12
5x = 20
x = 20/5
x = 4

21. 3 – 2 (1 – x) = 5 + 7(x – 3)
3 – 2 + 2x = 5 + 7x – 21
2x +1 = 7x – 16
2x – 7x = -17
-5x = -17
x = -17/-5
x = 17/5

23. 3z – 2 + 4(1 - z) = 5(1 - 2z) -12
3z – 2 + 4 – 4z = 5 - 10z -12
3z – 4z + 10 z = 5 – 12 +2- 4
9z = -9
z = 9/-9
z = -1

25. 1 -2 [4 - 3(x + 1)] =4 (x - 5) -1
1 - 2 [4 – 3x – 3] = 4x -20 – 1
1 - 8 + 6x + 6= 4x - 21
6x – 1 = 4x - 21
6x – 4x = -21 + 1
2x = -20
x = -20/2
x = -1027. [(3x + 7)/2] + [(1 + x)/3] = 0
(2 + 2x + 9x + 21)/ 6 = 0
(11x + 23)/6 = 0
11x/6 = -23/6 = 0
11x = (-23/6) (6)
11x = -23
x = -23/11

29. 1 – [(2u – 3)/4] = [(2 – 5u)/3] – 3u
(4 – 2u –3)/4 = (2 – 5u – 9u)/3
(1 – 2u)/4 = (2 – 14u)/3
(1 – 2u) (3) = (2 – 14u) (4)
3 – 6u = 8 – 56u
56u – 6u = 8 – 3
50u = 5
u = 5/50
u = 1/10








31. (1/3) (2y+1) + (y/2) = (2/5) (1-2y) –4
(2y/3) + (1/3) + (y/2) = (2/5) – (4y/5) – 4
2y + (y/2) – (4y/5) = (2/5) – 4 – (1/3)
(20y+5y-8y)/10 = (6-60-5)/15
17y/10 = -59/15
17y(15) = -59(10)
225y = -590
y = -590/225
y = 118/51...