Question

giải các bất phương trình sau:

a) 3x-5 > 2(x-1)+x

b)\(\left(x+2\right)^2-\left(x-2\right)^2>8x-2\)

c)3(4x+1) - 2(5x+2)≥ 8x-2

d)\(2x^2+2x+1-\dfrac{15\left(x+1\right)}{2}\le2x\left(x+1\right)\)

Answer 1

a) ta có : \(3x-5>2\left(x-1\right)+x\Leftrightarrow3x-5>2x-2+x\)

\(\Leftrightarrow-5>-2\left(vôlí\right)\) \(\Rightarrow x\in\varnothing\)

b) ta có : \(\left(x+2\right)^2-\left(x-2\right)^2>8x-2\Leftrightarrow8x>8x-2\)

\(\Leftrightarrow0>-2\left(đúng\forall x\right)\) \(\Rightarrow x\in R\)

c) ta có : \(3\left(4x+1\right)-2\left(5x+2\right)\ge8x-2\)

\(\Leftrightarrow12x+3-10x-4\ge8x-2\Leftrightarrow-6x\ge-1\Leftrightarrow x\le\dfrac{1}{6}\)

d) ta có : \(2x^2+2x+1-\dfrac{15\left(x+1\right)}{2}\le2x\left(x+1\right)\)

\(\Leftrightarrow2x^2+2x+\dfrac{2-15x-15}{2}\le2x^2+2x\)

\(\Rightarrow\dfrac{-15x-13}{2}\le0\Leftrightarrow-15x-13\le0\Leftrightarrow x\ge\dfrac{-13}{15}\)