Question

Giải các bất phương trình sau:

1. 12-2.(2x+5) > 3.(3-x)

2. 2.x-13/2 >=0

3. 6x + x.(3-2x) < -x.(2x-4) + 1

Answer 1

1) 12-4x-10>9-3x

=> 2-4x>9-3x

=> -4x+3x>9-2

=>-x>7 => x<7

2) \(2x-\dfrac{13}{2}>=0\)

=> \(2x>\dfrac{13}{2}\) => x>\(\dfrac{13}{4}\)

3)6x+3x-\(2x^2\) < \(-2x^2\) +4x+1

=> 9x-\(2x^2\) <\(-2x^2\) +4x+1

=>5x<1

=>x<\(\dfrac{1}{5}\)

Answer 2

1) 12-2(2x+5)>3(3-x)

<=> 12-4x-10>9-3x

<=> -4x+3x>9-12+10

<=> -x>7

<=>x<-7

=>S={x|x<-7}

2) 2x-\(\dfrac{13}{2}\)≥0

=>4x-13≥0

<=> 4x≥13

<=>x≥\(\dfrac{13}{4}\)

=>S={x|x≥\(\dfrac{13}{4}\)}

3) 6x+x(3-2x)<-x(2x-4)+1

<=>6x+3x-2x²<-2x²+4x+1

<=>6x+3x<4x+1

<=>6x+3x-4x<1

<=>5x<1

<=> x<\(\dfrac{1}{5}\)

=>S={x|x<\(\dfrac{1}{5}\)}