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Soluciones de Ecuaciones Algebraicas

The document contains examples of solving first and second degree equations. For first degree equations, the solutions are provided. For second degree equations, the solutions are also provided in most cases. The document contains examples of solving linear and quadratic equations step-by-step to find the solution(s).

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Leonardo Da Greco
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82 views5 pages

Soluciones de Ecuaciones Algebraicas

The document contains examples of solving first and second degree equations. For first degree equations, the solutions are provided. For second degree equations, the solutions are also provided in most cases. The document contains examples of solving linear and quadratic equations step-by-step to find the solution(s).

Uploaded by

Leonardo Da Greco
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
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ECUACIONES DE 1º GRADO

1. 2x-34=-20 Sol: x=7 2. 9x+8=7x+6 Sol: x=-1


3. 4x+3=3x+5 Sol: x=2 4. 7x+9=3+9x Sol: x=3
5. x-8=2x-11 Sol: x=3 6. x+1=2x-7 Sol: x=8
7. 6x+6=4+8x Sol: x=1 8. 9+9x=17+5x Sol: x=2
9. 2x+3=3x Sol: x=3 10. 25-2x=3x+20 Sol: x=1
11. 4x+1=3x+3 Sol: x=2 12. 5x-3=10x-6 Sol: x=3/5
13. 1+8x=-16x+31 Sol: x=5/4 14. 5x-11=15x-19 Sol: x=4/5
15. 12x-48=-15x-30 Sol: x=2/3 16. 2x+17=3x+7 Sol: x=10
17. 10-5x=x-2 Sol: x=2 18. 70-3x=4x Sol: x=10
19. 48-3x=5x Sol: x=6 20. -4x+30=-3x-10 Sol: x=40
21. 10x-15=4x+27 Sol: x=7 22. x-3(x-2)=6x-2 Sol: x=1
23. 3x+1=6x-8 Sol: x=3 24. 3x-7=2(x+1) Sol: x=9
25. 47-3x=5+11x Sol: x=3 26. 2(2+4x)=3+12x Sol: x=1/4
27. 30-9x=-7x+21 Sol: x=9/2 28. 5x=7(5x-3)+3 Sol: x=3/5
29. 3x-10=2x+1 Sol: x=11 30. 2(x-5)=3x-17 Sol: x=7
31. 25-2x=3x-35 Sol: x=12 32. 2+5(x-13)=x-3 Sol: x=15
33. 75-5x=3x+3 Sol: x=9 34. 2x-1=3(2x-15) Sol: x=11
35. 5+8x=2x+20 Sol: x=5/2 36. 2(x-2)=-(4-x) Sol: x=0
37. 2y-3=y+5 Sol: y=8 38. 2(3x-49)=-x+14 Sol: x=16
39. 2-6x=3x-1 Sol: x=1/3 40. 20=2x-(10-4x) Sol: x=5
41. 60x-1=3(1+12x) Sol: x=1/6 42. 5(x-1)+10(x+2)=45 Sol: x=2
43. 2x+3(2x-1)=x+67 Sol: x=10 44. 12x+3(2x-4)=60 Sol: x=4
45. 3-2x(5-2x)=4x2+x-30 Sol: x=3 46. 3x-(x+1)=x-2 Sol: x=-1
47. 3[2x-(3x+1)]=x+1 Sol: x=-1 48. x-3(x+5)=3x+10 Sol: x=-5
49. (x-15)=3(x-19) Sol: x=21 50. 3(2-x)=18x-1 Sol: x=1/3
51. 3(x+4)=4x+1 Sol: x=11 52. 10+5(x-3)=3(x+1) Sol: x=4
53. 2(3-4x)=2x-9 Sol: x=3/2 54. 10-9x=4(x-4) Sol: x=2
55. 2(3x+2)=4[2x-5(x-2)] Sol: x=2 56. 15x=2(1+9x)-3 Sol: x=1/3
57. 3(12-x)-4x=2(11-x)+9x Sol: x=1 58. x+3=3(2x-4) Sol: x=3
3x x x -6
59. + 2= x + 4 60. x - 8 = -
2 2 3
3x x  x+5 
61. x - = + 3 62. 2  = x + 3
4 7  3 
9x 2x 1 5x 3x
63. - 6= + 64. - = x - 11
4 3 3 6 4
3x 2x 5
65. - 7= + 1 66. x - 10 = (x - 6)
5 6 9
x 2x 3x x
67. + x = 10 + 68. + 1 = 12 -
3 9 2 3
x x 5x - 6
69. + = x - 3 70. 4x - 7 =
5 2 4
x+2 2x - 10 7
71. = 5x - 4 72. =
3 3x - 20 8
x 3x x 13 5x 5
73. + + x = 21 74. - = -
4 6 4 6 2 6
x x x x x
75. + + = 94 76. + 10 = + 16
3 4 5 3 5
x -7 10 x
77. = - 3 78. 3x - 9 + = 2x - 3
x+3 x+3 5
3x
_ 12 x 2x x
79. 5 80. + 5= - 2 -
=6 4 5 30
x +1
3 x 5x - 2x + 18
81. = - 1 82. - 5 (x - 20) =
x+1 x - 1 8 6
x +1 x 7-x x-3
83. x + =x + 84. 3x - = -1 + + 2x
5 2 8 4
3x 2x 5x x +1 3+ x x
85. 8 - + - =-9 86. + =1 +
10 4 8 2 6 3
3x 3x x 10 3 + 4x
87. - 2 + - =0 88. + =3
5 2 10 x+5 x+5
x+2 x + 3 2x + 2 7x - 3 3x - 1 5x - 1
89. - = 2 90. - =
x -1 x+1 x -1 6 4 4
4x - 3 3x - 1 4x - 2 3 (x + 1) x+3 3 - 7x
91. - = - 1 92. - + x = 2x +
6 4 3 4 6 12
2x x x 15 5
93. - 2 - = - 3 94. - =0
5 3 10 x + 10 x+2
2 3x - 3 2 7 2x + 1 3x 3x - 2
95. + 2 = + 96. - - 2=
x +1 x -1 x -1 x+1 4 9 4
5 3 3 5 15 12x + 6 18
97. - - 2 = 98. - 2
=
x -1 x+4 x + 3x - 4 x - 1 x-2 x -4 x+2
2
b - ab
99. (a + x) (b - x) - a (b + a) + x 2 + a 2 =
a
1 1 1 x 1 + x
100. + = 2 2 101. - 2=
x-a x+a x - a 2a 2
x +1
1+
x -1 = 2 x x-5 1 5x - 2
102. 103. + - x=
x -1 3 2 4 2
2 -
x +1
x-3 3 (x - 2) x - 3 - (x + 2) x-3 x-3 x-3 x+3
104. - = 105. - = -
3 2 2 5 2 3 2
x +1 5+ x 9 - 2x x+2 x-2
106. + =1 + 107. x (x - 2) - - = (x - 2 )2 - 4
2 6 3 3 2
2
x+2 x-2 x - 2x + 1 3
108. x (x - 2) - - = (x - 2 )2 - 4x 109. =
3 2 x (x + 1) (x - 1) 2x

Sol: 59. x=4; 60. x=12; 61. x=28; 62. x=1; 63. x=4; 64. x=12; 65. x=30; 66. x=15; 67. x=9; 68. x=6; 69.
x= 10; 70. x=2; 71. x=1; 72. x=12; 73. x=12; 74. x=-16/27; 75. x=120; 76. x=45; 77. x= 2; 78. x=5; 79. x=5;
80. x=60; 81. x=2; 82. x=24; 83. x=2/3; 84. x=-1; 85. x=40; 86. x=0; 87. x=1; 88. x=2; 89. x=3; 90. x=0; 91.
x=1; 92. x=0; 93. x=30; 94. x=2; 95. x=0; 96. x=-15/7; 97. x=0; 98. x=4; 99. x=b/a; 100. x=1/2; 101. x=5a/(1-
a); 102. x=3; 103. x=-18/23; 104. x=27/7; 105. x=51/2; 106. x=2; 107. x=-2/7; 108. x=22/31; 109. x=-5
ECUACIONES DE 2º GRADO

110. x2-7x+12=0 Sol: x=3; x=4 111. x2-9x+18=0 Sol: x=3; x=6
112. x2-5x+6=0 Sol: x=2; x=3 113. x2+8x+15=0 Sol: x=-5; x=-3
114. x2-6x-27=0 Sol: x=-3; x=9 115. x2-6x+9=0 Sol: x=3
116. x2+6x=-9 Sol: x=-3 117. 4x2+4x=3 Sol:x=1/2;x=-3/2
118. x2-9x+14=0 Sol: x=2; x=7 119. x2-6x+8=0 Sol: x=4; x=2
120. 2x2+10x-48=0 Sol: x=3; x=-8 121. x2-x=20 Sol: x=-4; x=5
122. x2=5x+6 Sol: x=6; x=-1 123. 2x2-5x+3=0 Sol: x=1; x=3/2
124. x2+10x+25=0 Sol: x=-5 125. x2+9=10x Sol: x=1; x=9
126. 3x2-39x+108=0 Sol: x=4; x=9 127. 2x2-9x+9=0 Sol: x=3; x=3/2
128. 3x2+2x=8 Sol: x=-2; x=4/3 129. 4x2+12x+9=0 Sol: x=-3/2
130. 5x2+1=6x Sol: x=1; x=1/5 131. 6x2+1=5x Sol:x=1/2; x=1/3
132. 6x2-6=5x Sol: x=-2/3; x=3/2 133. 2x2+7x+6=0 Sol: x=-2; x=-3/2
134. x2=2x+3 Sol: x=-1; x=3 135. 4x2+3=8x Sol:x=1/2; x=3/2
136. x2-x+1/4=0 Sol: x=1/2 137. 3x2-16x+5=0 Sol: x=5; x=1/3

x
2
3x + 2 (x - 3 )2
138. 1 - - =1 139. - x + x 2 = x - (x - 2)
3 3 2
1 3 x-1
140. + 3x + 3 x 2 - 2 = + 3 x 2 141. (x - 3 )2 - = 2x
x-1 x -1 3
x-3 1 2 1
142. - = 3x 143. x - + = 5x + 5
3 x -1 x 2x
x-3 5 3 8
144. + 3x - = 2x - - 3 145. 3x - + (x - 1 )2 = 3(x - 2) - (x - 5)
x x x x
x (x - 3) 2
146. (x - 3) (x - 2) + = (x - 2 )
2
x+2 (x - 2) (x + 2) 2
147. (x - 2) x - - = (x - 2 ) - 4
3 2
2 x-2
148. (x - 3 ) - + (3 - x) (x - 1) = (x - 2 )2
3
x -1 3+ x x -1 3+ x
149. - =2 150. - =2
x +1 x x +1 x -1
1 2 2x
151. x + =4 152. x 2 - x = -
x-2 9 3
2
x 5x 2
153. + 2= 154. x + = 3
3 3 x
4x - 8 x 3 2x + 9
155. x - 2 = 156. + =
x 2 x x
6x  x
157. 2x - 2 = - 5 158. x (x + 1) -  x +  = 0
x -1  2
3 1 + 3x x + 4 4x + 4 2- x
159. 3x + 1 - = 160. 2 + = +
x 4 3 3 x-3
1 6 2x - 3
161. x + = 162. x - 2 =
x 3x x
x 2 3x + 10 2x + 1
163. + = 164. x + 3 = 165.
3 x 3x x -1
x-3 x-3
3 1 -
1
= 2 4 =- 1
x + x 1
166. x - x
x +1
2 + x -1
x-2 1 -
x +1
Soluciones: 138. x=-2, x=-1; 139. x=1, x=5/3; 140. x=5/3, x=0; 141. x=4/3, x=7; 142. x=5/8, x=0; 143.
x=-3/4, x=-1/2; 144. x=-5, x=1; 145. x=-2, x=2; 146. x=1, x=4; 147. x=-2/3, x=4; 148. x=-1, x=8/3; 149. x=-3,
x=-1/2; 150. x=-3, x=0; 151. x=3; 152. x=-1/3, x=2/3; 153. x=2, x=3; 154. x=1, x=2; 155. x=4, x=2; 156. x=-2,
x=6; 157. x=-1/2, x=3; 158. x=0, x=1/2; 159. x=1, x=-4/3; 160. x=2, x=4; 161. x=1, x=-1; 162. x=3, x=1; 163.
x=-1, x=4; 164. x=-2, x=2; 165. x=1/2, x=2/3; 166. x=-1; x=2
ECUACIONES IRRACIONALES

1. x + x = 30 2. x + 1 = x+9 3. 7 - 3x - x = 7
4. x + 4 = 3 - x -1 5. 5 x + 3 = 2x 6. 3 6x + 1 - 5 = 2 x
x
7. 4x + 5 - 3x + 1 = 1 8. 2x - 1 + x+4 = 6 9. 1 + x+1 =
3
10. x3 - 2 x = x 11. x - 3 + x + 4 = 4x + 1
12. 2 x + 4 = 5 x + 4 13. x 2 + 3x + 7 = 5 14. 3 - x = x + 1
15. 2 2x - 1 = 6x - 5 + 2x - 9 16. 2x + 5 + 6 = 3x + 3
17. 3x + 10 = 1 + 3x + 3 18. 3x - 2 - 4 = 0 19. 2x + 1 = x - 1
1 21
20. 2x - 1 + 2x + 1 = 21. - 6x + 1 = 2 3x
2x - 1 6x + 1
3 6 2 =
3
22. = 23. 2 + 2x
x 3x + 4 x
24. x + 6 + x + 11 = 5 - 10 x 25. 9 15 - x = 6 2x + 3
Soluciones:
1. x=25, x=36; 2. x=16; 3. x=-3, x=-14; 4. x=13/9;
5. x=9, x=1/4; 6. x=8, x=1/2; 7. x=5, x=1; 8. x=5, x=221;
9. x=15, x=0; 10. x=0, x=3;11. x=12; 12. x=12;
13. x=3, x=-6; 14. x=1, x=4; 15. x=5; 16. x=2/9, x=2;
17. x=2; 18. x=6; 19. x=4, x=0; 20. x=5/8;
21. x=4/3; 22. x=4; 23. x=4, x=1; 24. x=-2, x=3/7;
25. x=-1

ECUACIONES BICUADRADAS Y BICÚBICAS

1. x4-5x2+4=0 2. x4+2x2-3=0 3. x6-9x3+8=0


4. x6-26x3-27=0 5. 6x4+2x2-8=0 6. x4-4x2=0
7. 4x4-17x2+4=0 8. 9x4-3x2+4=0 9. x4-6x2-27=0
10. x6+7x3-8=0 11. x4-2x2-8=0 12. x6+28x3+27=0

Soluciones:
1. x=1, x=2; 2. x=1; 3. x=2, x=1; 4. x=-1, x=3;
5. x=1; 6. x=0, x=2; 7. x=2, x=1/2 8. x=1/3, x=2
9. x=3 10. x=1, x=-2 11. x=2 12. x=-1, x=-3

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