Question

Giải các bất phương trình sau :

a) \(4x-8\ge3\left(3x-1\right)-2x+1\)

b) \(\left(x-3\right)\left(x+2\right)+\left(x+4\right)^2\le2x\left(x+5\right)+4\)

c) \(3x-\dfrac{x+2}{3}\le\dfrac{3\left(x-2\right)}{2}+5-x\)

d) \(x-\dfrac{x+2}{3}\ge3x-1+\dfrac{x}{2}\)

e) \(\dfrac{x\left(x+2\right)}{3}+\dfrac{\left(x-1\right)\left(x+2\right)}{2}\ge\dfrac{5\left(x+1\right)^2}{6}+1\)

f) \(\dfrac{x+5}{2012}+\dfrac{x+6}{2011}+\dfrac{x+7}{2010}>-3\)

Answer 1

a) 4x -8 ≥ 3(3x-1)-2x +1

⇒4x -8 ≥7x -2

⇒4x -7x ≥ -2 +8

⇒-3x ≥ 6

⇒x≤-2

Vậy bpt có nghiệm là:{x|x≤-2}

Answer 2

b) (x-3)(x+2)+(x+4)²≤ 2x (x+5)+4

⇔ x²+2x - 3x - 6 +x² + 8x +16≤ 2x² + 10x +4

⇔ x² +2x - 3x + x² + 8x - 2x²- 10x ≤ 4+6-16

⇔ -3x ≤ -6

⇔ x≥ 2

Vậy bpt có tập nghiệm là: {x|x≥2}