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. x -6x+9=0 Sol: x=3
2

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. 2x -9x+9=0 Sol:
2
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

2
3x + 2 (x - 3 )2
138. 1 - x - =1 139. - x + x 2 = x - (x - 2)
3 3 2
1 3 2 x -1
140. + 3x + 3 x 2 - 2 = + 3 x2 141. (x - 3 ) - = 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)
146. (x - 3) (x - 2) + = (x - 2 )2
2
x+2 (x - 2) (x + 2)
147. (x - 2) x - - = (x - 2 )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
5x 2
153. x + 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 =
3 x 3x x -1
x-3 x-3
3 1 -
1
= 2 4 =- 1
x 1
165. x + 166. x
x +1 x -
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
20. 2x - 1 + 2x + 1 = 21.
2x - 1
21
- 6x + 1 = 2 3x
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