Question

Gỉa phương trình :

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

b) 2 + \(\dfrac{2-3x}{5}\) \(\ge\) \(\dfrac{x+7}{2}\)

Answer 1

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

\(\Leftrightarrow\) 1 + 2x - 2 > 3 - 2x

\(\Leftrightarrow\) 2x + 2x > 3 - 1 + 2

\(\Leftrightarrow\) 4x > 4

\(\Leftrightarrow\) x > 1

Vậy bpt có n_o là S= {x|x >1}

b, 2 + \(\dfrac{2-3x}{5}\) \(\ge\) \(\dfrac{x+7}{2}\)

MTC là 10

\(\Leftrightarrow\) \(\dfrac{2.10}{10}\) + \(\dfrac{2\left(2-3x\right)}{10}\) + \(\dfrac{5\left(x+7\right)}{10}\)

\(\Leftrightarrow\) 20 + 2(2 - 3x) \(\ge\) 5(x + 7)

\(\Leftrightarrow\) 20 + 4 - 6x \(\ge\) 5x + 35

\(\Leftrightarrow\) -6x - 5x \(\ge\) 35 - 20 - 4

\(\Leftrightarrow\) -11x \(\ge\) 11

\(\Leftrightarrow\) x \(\le\) -1

Vậy bpt có n_o là S={x|x\(\le\) -1}

Answer 2

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

<=>1+2x-2>3-2x

<=>2x-1>3-2x

<=>4x>4

<=>x>1

b)2+\(\dfrac{2-3x}{5}\)\(\ge\)\(\dfrac{x+7}{2}\)

<=>20-2(2-3x)\(\ge\)5(x+7)

<=>20-4+6x\(\ge\)5x+35

<=>6x+16\(\ge\)5x+35

<=>x\(\ge\)35-16

<=>x\(\ge\)19