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ECUACIONES DE PRIMER GRADO 1. 5x-(3x-1)=4-2x 5x-3x+1=4-2x 5x-3x+2x=4-1 4x=3 X=3/4 2. 4x-[2x-(3x-1)]=4-2x 4x-[2x-3x+1]=4-2x 4x-2x+3x-1=4-2x 4x-2x+3x+2x=4+1 7x=5 X=5/7 3. 3(x-2)= -5 (4-2x) 3x-6= -20 + 10x 3x-10x=-20+6 -7x=-14 X=-14/-7 = 2

4. 5(3x-8) – 4(2x-6) – 9x =2 15x-40-8x+24-9x=2 15x-8x-9x=2+40-24 -2x=18 X=18/-2=-9 5. 2 – 3(x-7) – 7x = 4 (x-2) + 8 2-3x+21-7x=4x-8+8 -3x-7x-4x=-8+8-2-21 -14x=-23 X= -23/-14=23/14 6. x – 4(2x-6) – (x-8)= 0 x-8x+24-x+8=0 x-8x-x=0-24-8 -8x=-32 X=-32/-8 = 4

7. 3(x+6)= -2(5-x) 3x+18= -10 + 2x 3x-2x= -10-18 x=-28 8. -4(x-1)=7(1-x) -4x+4=7-7x -4x+7x=7-4 3x=3 X=3/3=1 1


9. x-15=3(2x-1)-(x-4) x x 10. 5 4 5

X = 100

x 2 3 12. 4 11.

13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

x 4 x 2 2

x 8 1 5 x

7

3x 10 1 x6 2 x 6 2x+1= 5 x x 4 3 2 3 x 5 x = 5 4 2 6 4x 12 =x–5 4 x 3 =4 ( 2) x 4 x 3 x 1 1 5 4 2 1 3 5x – ( x) x 3 4 2( x 2) 5x x 3 4 x 32 x 7 40 x 3 176 x 5 3x 7 1 3x 17

25. 2 ( 5x+1) – 2(7x-9)= 10(3x+2) + 11(5-3x)-61 x 1 x 6 26. x 1 2 3 x x 3 2x 5 27. 1 6 4 3 3( x 8) 5( x 4) 28. x 10 16 12 x 2 3x 5 29. 1 5x 3 3 6 x 3x 10 30. 2 4 3 2


31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45.

1 1 (3x 5) ( x 4) 1 4 6 1 5 2 ( x 3) ( x 1) 3 6 3 6 x 3x 10 2 4 3 1 1 ( x 3) ( x 4) 1 2 3 x 2 3 x 2x 1 4 2 3 4x x x39 x 5 2 5x 9 4x 5 9 x 8 10 2 4x – 2 (x+8) = 2x + 3 ( 4 – x) 2 1 1 x= -x 3 4 6

X=8 X=30 X= 5 X = 10 1 X= 4 2 X= 0

2x – 3 (x – 1) = 5 – x

x 1 x 2 x 3 =0 2 3 4 3x – (2x – 5) = 12 1 1 (2 x 11) (5 6 x) 7 x 5 2 ( x 4) 2 ( x 5) 2 15 1 1 1 48 x 16

X= 11 X=7

3 2

X= X= -3 X= 24

46.

5 – (1+3x) – 2 (x-1) = 0

47.

2x 4 x 1

4 5

X= 4

48.

2x – 2 (x – 3) = 12

X=

49.

2x – [3 – 2 (5x - 4) ] = 6x – 2

50.

4x + 7 = 2 – 3 (1 + 3x)

51.

4 1 2 x

52.

– 8 (10 – x) = - 6

53.

5x + 2 = -10

54.

1-

55.

2x 5 4x 7 x 40 10 3x 2x 1 5 4 3

X=

6 5

6 0 X=

X= -

8 13

X= 4

37 4 12 X= 5 51 X= 158 X=

2 x 3

1 2

X= 48 3

3 2


1 1 1 22 X= (2 x 11) (5 6 x) 7 x 1 5 2 2 5 49 3 57. X= -7 7( x) 10( x 3) 2 4 4 4x 1 1 58. X= -2 5 x 8( x ) 4x 3 3 2 3 1 1 22 59. X= (5 x 1) ( x 3) x 5 7 5 3x 5 21 x 1082 114 60. X= 5 x 39 8 8 3 121 121 5x 3 8 x 7 x 4 61. (4 x 2) 7 3 2 5 1 3x 2 1 62. 2x2( x 3) 10 3 5 3x 4 1 63. 5x 6 2 2 x 8 3x x 5 64. 1x 21 7 3 x 1 2 5 65. x 3 1 2 3 4 1 66. (2 x 1) ( x 3) x 2 4 5 2 5x 2 2 67. 3x 1 7 68. 3(2x+1) – 5 =14 – (x+4) 3 2x 1 x 69. 1=x15 3 70. (5x-4)(8x-9) – (10x-9)(4x+3) = 3(4-6x) -2 x 2 x 3 71. x–10 2 3 DE SEGUNDO GRADO 72. 2x 2 - x = 0 73. x 2 5x 0 74. 4x 2 - 16 = 0 75. 4x 2 - 32x = 0 76. 8x 2 - 2x = 0 77. 3x 2 = 27 78. 9 = 3 (x 2 1) 56.

79. 80. 81. 82. 83. 84. 85.

2

x - 16x = 0 3x 2 27 0 11x 2 - 44x =0 7x = 21 x 2 9x 2 +26= 3x 2 +80 7x 2 +21x = 0 5x 2 + 40x = 0 4


86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123.

x 2 = 7x x 2 + 3x = 0 2x 2 - 1 = 1 3(x+1) – x(x-1) = 4x 2x 2 - 1= -1 2 x 2 3x 0 3 2 2 x 2 4 3x 2 7 11 5 3 15 x 3 x 12 3 x 12 x 7 11 5 2 3x 9x 2 8 x 2 15x 50 0 x 2 12x 35 0 16x 2 - 104x+25=0 x 2 6x 8 0 3x 2 -10x+3=0 x 2 9 x 20 0 6x 2 5x 1 0 7x 2 10 101x 3x 2 2x 2 1 1 x x 2 x 2 100x 2500 2 x 8 x (8 x 17) 0

8x 2 20x 12 2 x 50 49 2x 24x+35=-2x 2 -35 x 2 -x=30 11x (11x-4)=5 8x 2 +1=-6x 2x 2 - 1= 3x – 2x 2 5x 2 3x 2 0 x 2 5x 6 0 6x 2 2x 4 3x 2 2x 4 3x 3x 2 5x 2 - 2x=3-3x 2 16x 2 60x 100x 9 2x 2 19x 9 0 (x-1) 2 =16 2(x 2 +1) -5x =0 2 11x = 3 (2x +1) 3(x-1)(x+1)=8x 7x 124. (x-1)(x+1) = 12 2 2 x) 125. 15= 4(3x 126. (2x-1) 2 = 25 5


1 127. (3x- ) 2 49 2 128. 3x(5x-1) = 4(x+9) 129. 20x 2 20x 4 5x 2 130. 10x 2 15 3x (6 x 2

5 x)

2

131. x 7 x 18 132. x-6+2x 2 4 x 2 8x ( x 1) 2 133. (3x-2) 2 1 134. (x-3) 2 2( x 2 9) 0 135. (x-1)(x-2) - 12 = 0 12 136. 2+ x 3 x 3 2 x 20 137. 2= x 2x 8 6 x 33 138. 15 ( x 5) x x 1 2x 139. x 2 2 3 3 12 140. x = 8 x x 2 1 141. 9 x 2 x 5 5 142. 2 x 2 2 x 36 x 2 64 143. 14 8 6

3x 2 108 4 x 2 256 24 24

336 24

7x 2 = 336+364 7x 2 = 700 100 = 10 X=

144.

3x 4 4x 1 5 x 16 6 x 11 18x 2 - 33x – 24x + 44 = 20x 2 - 64x +5x – 16 18x 2 - 20x 2 -33x-24x+64x-5x+44+16=0 -2x 2 + 2x+60=0

6


3 x 2 4 5 x 5 2 3x x 10 4 x 5x 5x 5x 2 -x + 3x + 4x – 10 =0 - x 2 +7x-10=0 x 2 -7x+10=0

145.

x=

7

49 40 2

x1 5

7 3 2

x2 2

146. 12x 2 60 0 147. (x+4) 2 8x 24 x 2 8x 16 8x 24 x 2 + 16 – 24 = 0 x2 - 8 = 0 8 x= 148. 6x 2 17x 14 0 x 2 3 1 149. 2 x x 3 3x 2 12 18 2 x 6x 6x 6x 6x 3x 2 + 2x – 6 = 0 2 4 4.3.( 6) X= = 6

2

76 6

150. 4x(x+2)-5=12-(x-4) 2 4x 2 + 8x – 5 = 12 – (x 2 - 8x + 16) 4x 2 + 8x – 5 = 12 - x 2 + 8x – 16 4x 2 + x 2 + 8x – 8x – 5 – 12 + 16 = 0 5x 2 - 1 = 0 1 X= 5 2 151. x -6x=0 152. 4x 2 3x 0 153. (x-1)(x+3)-(x-2) 2 x 2 1 x 2 + 3x – x – 3 – (x 2 - 4x + 4) = x 2 + 1 x 2 + 2x – 3 - x 2 + 4x – 4 = x 2 + 1 - x 2 + 6x – 8 = 0 x 2 - 6x + 8 = 0 x= 4 6 36 32 6 2 x= x= 2 2 2 154. 2x 2 18 0 155. 3x 2 27 0 7


156. 157. 158. 159. 160. 161.

3 x 2 4 5 x 5 5 3 1 2 2 3 4x 6x 2 4x 16 0 4x 2 32x 0 5x 2 40x 0 9 = 3(x 2 1)

162. 2x 2 6x 0 163. (2x – 1) 2 25 6 x 33 164. 15 ( x 5) x 165. (x – 1) 2 0 166. (x – 2) 2 1 0 167. x (x-1)= x-5 3x 2 x 2 168. x 1 8 4 1 169. (x- )( x 5) 0 2 3 170. x+2= x 2 171. x 3( x 1) 5 2 x 172. x(x+3)+6= - 3 (x+1) 7x 6 173. x 2 x 4 5 5 x 174. x 2 x 4 8 2 175. 4x 2 50 50 4 x 16x 2 176. 0 4 177. (x-3)(x+3) = 0 2 178. 4x(x- ) = 0 3 1 179. (x- ) x =0 2

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