1) Resolver las siguientes ecuaciones:
- a) 2x - 20 = 100
- 2x = 100 + 20
- 2x = 120
- x = 120 / 2
- x = 60
- b) 1/2 * x - √100 = 3/5 * x + 18
- 1/2 * x - 10 = 3/5 * x + 18
- 1/2 * x - 3/5 * x = 18 + 10
- -1/10 * x = 28
- x = 28 / (-1/10)
- x = -280
- c) 3(5x + 8) - ³√144 = 27
- 15x + 24 - 6 = 27
- 15x = 27 - 24 + 6
- 15x = 9
- x = 9 / 15
- x = 3/5
- d) 2/3 * 3/5 + 3x = 6/5 - 2x
- 2/5 + 3x = 6/5 - 2x
- 3x + 2x = 6/5 - 2/5
- 5x = 4/5
- x = (4/5) / 5
- x = 4/25
2) Resolver las siguientes operaciones combinadas aplicando propiedades cuando sea necesario:
- a) ³√100 : 2² + 3⁵ : 3³ + √144 : (-4) =
- ³√100 = 4.64 (aproximadamente)
- 2² = 4
- 3⁵ = 243
- 3³ = 27
- √144 = 12
- (-4) = -4
- 4.64 / 4 + 243 / 27 + 12 / (-4) = 1.16 + 9 - 3 = 7.16
- b) 2⁵ : 2³ - √49.3 + (8.4 - 40) =
- 2⁵ = 32
- 2³ = 8
- √49.3 = 7.02 (aproximadamente)
- 8.4 - 40 = -31.6
- 32 / 8 - 7.02 - 31.6 = 4 - 7.02 - 31.6 = -34.62
- c) √100 - 6² + 2(3.7 - 4.5) =
- √100 = 10
- 6² = 36
- 3.7 - 4.5 = -0.8
- 10 - 36 + 2(-0.8) = 10 - 36 - 1.6 = -27.6
- d) 10⁶ : 10⁵ - 8.7 + √49.9 =
- 10⁶ = 1,000,000
- 10⁵ = 100,000
- √49.9 = 7.06 (aproximadamente)
- 1,000,000 / 100,000 - 8.7 + 7.06 = 10 - 8.7 + 7.06 = 8.36
3) Resolver las siguientes operaciones con fracciones:
- a) 5/6 * (-8/2) + 1/12 =
- (5/6) * (-8/2) = -20/12 = -5/3
- -5/3 + 1/12 = (-20 + 1) / 12 = -19/12
- b) 9/6 : (3/4 - 8/18) =
- 3/4 - 8/18 = (27 - 16) / 36 = 11/36
- 9/6 : 11/36 = 9/6 * 36/11 = (9 * 36) / (6 * 11) = 27/11
- c) 7/3 + 4/5 - 1/2 =
- 7/3 + 4/5 - 1/2 = (70 + 24 - 15) / 30 = 79/30
- d) 17/5 : 2² =
- 2² = 4
- 17/5 : 4 = 17/5 * 1/4 = 17/20
