Ecuaciones 1er grado

Ecuaciones de primer grado con una incógnita Fuente: Algebra de A. Baldor I 1. 2. 3. 4. 5. 6. 7. II 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. III 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. IV 1. 2. 3. 4. De coeficientes enteros 5x = 8x – 15 4x + 1 = 2 y – 5 = 3y – 25 5x + 6 = 10x + 5 9y – 11 = -10 + 12y 21 – 6x = 27 – 8x 11x + 5x – 1 = 65x – 36 8. 9. 10. 11. 12. 13. 14. 8x –4 + 3x = 7x + x + 14 8x + 9 – 12x = 4x – 13 – 5x 5y + 6y – 81 = 7y + 102 + 65y 16 + 7x – 5 + x = 11x – 3 – x 3x + 101 – 4x – 33 = 108 – 16x – 100 12 – 12x + 39x – 18x = 256 – 60x – 657x 8x – 15x – 30x – 51x = 53x + 31x – 172

De coeficientes enteros con uso de paréntesis x – (2x + 1) = 8 – (3x + 3) 15x – 10 = 6x – (x + 2) + (-x + 3) (5 – 3x) – (-4x + 6) = (8x + 11) – (3x – 6) 30x – (-x + 6) +(-5x + 4) = -(5x + 6) + (-8 + 3x) 15x + (-6x + 5) – 2 – (-x + 3) = - (7x + 23) – x + (3 – 2x) 3x + [-5x – (x + 3)] = 8x + (-5x – 9) 16x – [3x – (6 – 9x)] = 30x + [-(3x + 2) – (x + 3)] x – [5 + 3x – {5x – (6 + x)}] = -3 9x – (5x +1) – {2 + 8x – (7x – 5)} + 9x = 0 71 + [-5x + (-2x + 3) = 25 – [-(3x + 4) – (4x + 3)] –{3x + 8 – [-15 + 6x – (-3x + 2) – (5x + 4)] – 29} = -5 De coeficientes enteros conproductos x + 3(x – 1) = 6 – 4(2x + 3) 5(x – 1) + 16(2x + 3) = 3(2x – 7) – x 2(3x + 3) – 4(5x – 3) = x(x – 3) – x(x + 5) 184 – 7(2x + 5) = 301 + 6(x – 1) – 6 7(18 – x) – 6(3 – 5x) = -(7x + 9) – 3(2x + 5) – 12 3x(x – 3) + 5(x + 7) – x(x + 1) – 2(x2 + 7) + 4 = 0 -3(2x + 7) + (-5x + 6) – 8(1 – 2x) – (x – 3) = 0 (3x – 4)(4x – 3) = (6x – 4)(2x – 5) (4 – 5x)(4x – 5) = (10x – 3)(7 – 2x) (x + 1)(2x + 5) =(2x + 3)(x – 4) + 5 (x – 2)2 – (3 – x)2 = 1 14 – (5x – 1)(2x + 3) = 17 – (10x + 1)(x – 6) (x – 2)2 + x(x – 3) = 3(x + 4)(x – 3) – (x + 2) (x – 1) + 2 (3x – 1)2 – 5(x – 2) – (2x + 3)2 – (5x + 2)(x – 1) = 0 2(x – 3)2 – 3(x + 1)2 + (x – 5)(x – 3) + 4(x2 – 5x + 1) = 4x2 – 12 5(x – 2)2 – 5(x + 3)2 + (2x – 1)(5x + 2) – 10x2 = 0 x2 – 5x + 15 = x(x – 3) – 14 + 5(x – 2) + 3(13 – 2x) 3(5x – 6)(3x + 2) – 6(3x+ 4)(x – 1) – 3(9x + 1)(x – 2) = 0 7(x -4)2 – 3(x + 5)2 = 4( x + 1)(x – 1) – 2 5(1 – x)2 – 6(x2 – 3x – 7) = x(x – 3) – 2x(x + 5) – 2 Fraccionarias con denominadores monomios
x 1 +5 = −x 6 3 3 x 2x 1 − + =0 5 3 5 1 1 1 1 + − = 2x 4 10 x 5 x x x 5 +2− = − 2 12 6 4

5. 6. 7. 8.

3x 1 5 3x − + 2x = − 4 5 4 20 2 5 7 3 − = − +1 3 x x 10 2x x−4 −5 = 0 3 x + 2 5x x− = 12 2

Hernán Verdugo Fabianiwww.hverdugo.cl

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9. 10. 11. 12. 13. 14. 15. V 1. 2. 3. 4. 5.

5x − 1 3 = 4x − 3 5 8x − 3 10 x − = 2( x − 3) 4 x−2 x−3 x −4 − = 3 4 5 x −1 x − 2 x − 3 x −5 − − =− 2 3 4 5 7 − 5x x − (5 x − 1) − =1 10 5x − 6 1 2x − + ( x − 5) = −5 x 4 3 10 x + 1 16 x + 3 4− = 4x − 6 4 x−

16. 17.

7 x − 1 5 − 2x 4 x − 3 1 + 4 x 2 − = + 3 2x 4 3x 2 2 2x + 7 2( x − 4) 4 x − 6 7 x 2 + 6 − − = 3 5x 15 x 3x2
3 ⎛ 2x − 1 ⎞ 4 ⎛ 3x + 2 ⎞ 1 ⎛ x − 2 ⎞ 1 ⎟− ⎜ ⎜ ⎟− ⎜ ⎟+ =0 5⎝ 6 ⎠ 3⎝ 4 ⎠ 5⎝ 3 ⎠ 5 5+ x 1⎛ x⎞ 2 1⎛ 5x ⎞ = ⎜ 2 − ⎟ − + ⎜10 − ⎟ 4 3⎝ 2⎠ 3 4⎝ 3 ⎠

18.

19. 20.

3x − 1⎞ 2 ⎛ x + 2 ⎞ 1 ⎛ 2x − ⎜ 2x − ⎟= ⎜ ⎟− 8 ⎠ 3⎝ 6 ⎠ 4 ⎝

Fraccionarias con denominadores compuestos
3 3 + =0 5 2x − 1 2 3 = 4x − 1 4x + 1 5x + 8 5x + 2 = 3x + 4 3x − 4 10 x 2 − 5 x + 8 =2 5 x 2 + 9 x − 19 1 1 1 + = 3 x − 3 4 x +4 12x − 12

6. 7. 8.

x x 2 − 8x 7 − = 4 4x − 5 4 6 x − 1 3( x + 2) 1 + 3 x − = 18 5x − 6 9 5 x − 13 4 x + 5 2 − = 15 5 x − 15 3
1 2 1 2 3 3 − = − x − 1 x − 2 2x − 2 2x − 4 x + 6 x +1 x −5 x − = − x+2 x−3 x −1 x + 4

9. 10.

VI 1. 2. 3. 4. 5. VII 1. 2. 3. 4. 5.

Ecuaciones literales enteras a(x + 1) = 1 ax – 4 = bx – 2 ax + b2 = a2 – bx 3(2a – x) + ax = a2 + 9 ax – a(a + b) = -x – (1 +ab) Ecuaciones literales fraccionarias
m 1 2 − = x m m a b 4a + = x 2 x x 1− x 1 − 2 = 2a 2a a m n n + = +1 x m x a − 1 1 3a − 2 + = a 2 x

6. 7. 8. 9. 10.

m(n – x) – m(n – 1) = m(mx – a) x – a + 2 = 2ax – 3(a + x) – 2(a – 5) x(a + b) – 3 – a(a – 2) = 2(x – 1) – x(a – b) x2 + a2 = (a + x)2 – a(a – 1) (ax – b)2 – (x – a)2 – (a – b)2 = 0

6. 7. 8. 9. 10.

x−b x−a = 2− a b 4x 3 −3 = − 2a...