Question

1.Giải các phuong trình sau:

A. 5x -20 \(\le\)0

B.3x+7 > -7x+2

C. -9x-5 <4x +21

D. 3(2x-5) >8x-13

E. 2(3x-5) \(\ge\)5(2x+6)

F.\(\frac{2x-3}{4}\)\(\le\)\(\frac{3x+1}{6}\)

H.2x+3(x-3)\(\ge\)10x-(3x+2)

Help me

Answer 1

a) \(5x-20\le0\\ \Leftrightarrow5x\le20\\ \Leftrightarrow x\le\frac{20}{5}\\ \Leftrightarrow x\le4\)

b)\(3x+7>-7x+2\\ \Leftrightarrow3x+7x>2-7\\ \Leftrightarrow10x>-5\\ \Leftrightarrow x>-\frac{5}{10}\\ \Leftrightarrow x>-\frac{1}{2}\)

c)\(-9x-5< 4x+21\\ \Leftrightarrow-9x-4x< 21+5\\ \Leftrightarrow-13x< 26\\ \Leftrightarrow x>\frac{-26}{13}\\ \Leftrightarrow x>-2\)

d) 3(2x-5) >8x-13

<=> 6x -15> 8x-13

<=> 6x-8x>-13+15

<=>-2x>2

<=> x< -2/2

<=>x<-1

e) \( 2(3x-5) ≥ 5(2x+6)\\ \Leftrightarrow6x-10\ge10x+30\\ \Leftrightarrow6x-10x\ge30+10\\ \Leftrightarrow-4x\ge40\\ \Leftrightarrow x\le-\frac{40}{4}\\ \Leftrightarrow x\le-10\)

f) \(\frac{2x-3}{4}\le\frac{3x+1}{6}\\ \Leftrightarrow\frac{3.\left(2x-3\right)}{12}\le\frac{2.\left(3x+1\right)}{12}\\ \Leftrightarrow6x-9\le6x+2\\ \Leftrightarrow6x-6x\le2+9\\ \Leftrightarrow0x\le11\)

=>Luôn đúng => Bpt vô số nghiệm

Answer 2

h. Ta có : \(2x+3\left(x-3\right)\ge10x-\left(3x+2\right)\)

=> \(2x+3x-9\ge10x-3x-2\)

=> \(2x+3x-9-10x+3x+2\ge0\)

=> \(-2x-7\ge0\)

=> \(x\ge-\frac{7}{2}\)