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Ecuaciones

The document contains 107 math word problems involving equations of the first degree. Each problem provides the equation, the solution steps, and the solution. The problems cover a wide range of equation types including single-variable linear equations, multi-step equations, fractional equations, and equations involving grouping symbols.

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ALEJANDRA LANNE
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46 views5 pages

Ecuaciones

The document contains 107 math word problems involving equations of the first degree. Each problem provides the equation, the solution steps, and the solution. The problems cover a wide range of equation types including single-variable linear equations, multi-step equations, fractional equations, and equations involving grouping symbols.

Uploaded by

ALEJANDRA LANNE
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as 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: =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
+ 2= x + 4 60. x - 8=
2
-
3
3x x  x+5 
61. x -
4
=
7
+ 3 62. 2  3  = x + 3
 
9x 2x 1 5x 3x
63. 4
- 6=
3
+
3
64. 6 - 4 = x - 11
3x 2x 5
65. 5
- 7=
6
+ 1 66. x - 10 = 9 (x - 6)
x 2x 3x x
67. 3
+ x = 10 +
9
68. 2 + 1 = 12 - 3
x x 5x - 6
69. 5
+
2
=x - 3 70. 4x - 7 = 4
x+2 2x - 10 7
71. 3
= 5x - 4 72. 3x - 20
=
8
x 3x x 13 5x 5
73. 4
+
6
+ x = 21 74. 4 - 6 = 2 - 6
x x x x x
75. 3
+
4
+
5
= 94 76. 3 + 10 = 5 + 16
x -7 10 x
77. x+3
=
x+3
- 3 78. 3x - 9 + 5 = 2x - 3
3x
_ 12 x 2x x
79. 5 =6 80. 4 + 5=
5
- 2 -
30
x +1
3 x 5x - 2x + 18
81. x + 1 = x - 1 - 1 82. 8
- 5 (x - 20) =
6
x+1 x 7-x x-3
83. x + 5 = x + 2 84. 3x - 8 = - 1 + 4 + 2x
3x 2x 5x x +1 3+ x x
85. 8 - 10 + 4 - 8 = - 9 86. 2 + 6 = 1 + 3
3x 3x x 10 3 + 4x
87. 5 - 2 + 2 - 10 = 0 88. x + 5 + x + 5 = 3
x+2 x+3 2x + 2 7x - 3 3x - 1 5x - 1
89. x - 1 - x + 1 = 2 - 1 90. 6 - 4 = 4
x
4x - 3 3x - 1 4x - 2 3 (x + 1) x+3 3 - 7x
91. 6
-
4
=
3
- 1 92. - + x = 2x +
4 6 12
2x x x 15 5
93. 5
- 2 -
3
=
10
- 3 94. x + 10
x+2
- =0

2 3x - 3 2 7 2x + 1 3x 3x - 2
95. x +1
+ 2
= + 96. - - 2=
x -1 x -1 x+1 4 9 4
5 3 3 5 15 12x + 6 18
97. x -1
-
x+4
- 2 = 98. x - 2 - 2
=
x + 3x - 4 x -1 x -4 x+2
2
- ab
99. (a + x) (b - x) - a (b + a) + x2 + a 2 = b
a
1 1 1 x 1 + x
100. x-a
+
x+a
= 2 2 101. 2a - 2=
x -a 2
x +1
1 +
x -1 = 2 x x-5 1 5x - 2
102. x -1 103. 3 +
2
-
4
x=
2
2 -
x +1
x-3 3 (x - 2) x - 3 - (x + 2) x-3 x-3 x-3 x+3
104. - = 105.
5
-
2
=
3
-
2
3 2 2
x +1 5+ x 9 - 2x x+2 x-2
106. 107. x (x - 2) - 3 - 2 = (x - 2 ) - 4
2
+ =1 +
2 6 3
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=0Sol: 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=0Sol: 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 2
3x + 2 (x - 3 )
138. 1 - x - =1 139. - x + x 2 = x - (x - 2)
3 3 2
1 3 x-1
140. 141. (x - 3 )
2
+ 3x + 3 x 2 - 2 = + 3 x2 -
= 2x
x-1 x -1 3
x-3 1 2 1
142. 3
-
x -1
= 3x 143. x - x + 2x = 5x + 5
x-3 5 3 8
144. 145. 3x - x + (x - 1 ) = 3(x - 2) - (x - 5)
2
+ 3x - = 2x - - 3
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
x-2
148. (x - 3 )
2
- + (3 - x) (x - 1) = (x - 2 )2
3
x -1 3+ x x -1 3+ x
149. x + 1 - x = 2 150. x + 1 - x - 1 = 2
1 2 2x
151. x + x - 2 = 4 152. x 2 - x = 9 - 3
2
5x 2
153. x + 2 = 154. x + x = 3
3 3
4x - 8 x 3 2x + 9
155. x - 2 = x 156. 2 + x = x
6x  x
157. 2x - 2 = x - 1 - 5 158. x (x + 1) -  x + 2  = 0
 
3 1 + 3x x+4 4x + 4 2- x
159. 3x + 1 - x = 4 160. 2 + 3 = 3 + x - 3
1 6 2x - 3
161. x + x = 3x 162. x - 2 = x
x 2 3x + 10 2x + 1
163. 3 +
x
=
3x
164. x + 3=
x -1
x-3 x-3
3 1 -
= 2 4 1
1 x =-
165. x +
x +1 166. 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 = 2 x 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. 2
x + 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 =
2x - 1
21. 6x + 1
- 6x + 1 = 2 3x

3 6 3
2 =
22. x
=
3x + 4
23. 2 + 2x
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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