Bài 3: Phương trình đưa được về dạng ax + b = 0

Δ=1^2-4*1*4=-15<0

=>PTVN

\(x^2-2x=0\)

\(\Leftrightarrow x\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-2=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)

\(x^2-2x=0\)

\(\Leftrightarrow x\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-2=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)

\(S=\left\{0;2\right\}\)

=>-3x>=-9

=>x<=3

\(-3x+9\ge0\)

\(\Leftrightarrow-3x\ge-9\)

\(\Leftrightarrow x\le3\)

-3x + 9 ≥ 0

⇔-3x ≥ -9

⇔ x \(\le\) -9/-3

⇔ x \(\le\) 3

\(5x-4\left(6-x\right)\left(x+3\right)=\left(4-2x\right)\left(3-2x\right)+2\)

\(\Leftrightarrow5x-4\left(18+3x-x^2\right)=12-14x+4x^2+2\)

\(\Leftrightarrow5x-72-12x+4x^2-14+14x-4x^2=0\)

\(\Leftrightarrow7x-86=0\)

\(\Leftrightarrow x=\dfrac{86}{7}\)

\(5x-4\left(6-x\right)\left(x+3\right)=\left(4-2x\right)\left(3-2x\right)+2\\ < =>5x-4\left(6x+18-x^2-3x\right)=\left(12-8x-6x+4x^2\right)+2\)

\(< =>5x-24x-72+4x^2+12x=12-8x-6x+4x^2+2\)

\(< =>4x^2-4x^2+5x-24x+12x+8x+6x=12+2+72\)

\(< =>7x=86\\ < =>x=\dfrac{86}{7}\)

\(5x-4\left(6-x\right)\left(x+3\right)=\left(4-2x\right)\left(3-2x\right)+2\)

\(\Leftrightarrow5x-4\left(6x+18-x^2-3x\right)=\left(12-8x-6x+4x^2\right)+2\)

\(\Leftrightarrow5x-4\left(-x^2+3x+18\right)=4x^2-14x+12+2\)

\(\Leftrightarrow5x+4x^2-12x-72=4x^2-14x+14\)

\(\Leftrightarrow5x+4x^2-12x-72-4x^2+14x-14=0\)

\(\Leftrightarrow7x-86=0\)

\(\Leftrightarrow7x=86\)

\(\Leftrightarrow x=\dfrac{86}{7}\)

\(\text{Vậy phương trình trên có tập nghiệm là }S=\left\{\dfrac{86}{7}\right\}\)

Nếu pt ra 0x = 0 thì kết luận pt vô số nghiệm, còn nếu 0x ≠ 0 thì kết luận là vô nghiệm.

\(x^5+x^4+x^3+x^2+x=0\)

⇔\(\left(x^5+x^4\right)+\left(x^3+x^2\right)+\left(x+1\right)=0\)

⇔\(x^4\left(x+1\right)+x^2\left(x+1\right)+\left(x+1\right)=0\)

⇔\(\left(x+1\right)\left(x^4+x^2+1\right)=0\)

⇔ \(\left[{}\begin{matrix}x+1=0\\x^4+x^2+1=0\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}x=-1\\x\in\varnothing\end{matrix}\right.\)

\(a,\left(x-1\right)^2-4=0\)

\(\Leftrightarrow\left(x-1\right)^2=4=\left(\pm2\right)^2\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=2\\x-1=-2\end{matrix}\right.\)               \(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)

Vậy tập nghiệm của phương trình là \(S=\left\{3;-1\right\}\)

__________________________________

\(b,\dfrac{x+1}{x-1}=1+\dfrac{1}{x-1}\)

\(\Leftrightarrow\dfrac{x+1}{x-1}=\dfrac{x-1}{x-1}+\dfrac{1}{x-1}\)

\(\Leftrightarrow x+1=x-1+1\)

\(\Leftrightarrow x-x=-1-1+1\)

\(\Leftrightarrow0=-1\) (vô lý)
Vậy phương trình vô nghiệm.

`a, -2x + 8 = 0`

`<=> 8 = 2x`

`<=> x = 4`

Vậy PT có nghiệm là `4`.

`b, -3x+1 =0`

`=> 1=3x`

`<=> x = 1/3`

Vậy PT có nghiệm là `1/3`

`c, -2x + 5= 0`

`<=> 2x = 5`

`<=> x = 5/2`

Vậy PT có nghiệm là `5/2`

`d, -3x-5=0`

`<=> 3x = -5`

`<=> x = -5/3`

Vậy PT có nghiệm là `-5/3`

`e, 4x-10=0`

`<=> 4x=10`

`<=> x = 5/2`

Vậy PT có nghiệm là `5/2`

`f, 22x+11=0`

`<=> 22x=-11`

`<=> x=-11/22`

`<=> x=-1/2`

Vậy PT có nghiệm là `-1/2`

12)  -2x + 8 = 0 
  <=> -2x = -8
 <=> x=4 
21) 2x + 3=0
 <=> 2x = -3
<=> x = -3/2 

18: =>3x-x=3+1

=>2x=4

=>x=2

19: =>-7x+3x=9-15

=>-4x=-6

=>x=1,5

20: x=18+3=21

21: =>2x+5x=15-1

=>7x=14

=>x=2

22: =>3x-2x=5+2

=>x=7

23: =>4x-3x=-5

=>x=-5

24: =>-23x-x=-19-5

=>-24x=-24

=>x=1

15: =>-3x+7-9+x=0

=>-2x-2=0

=>2x+2=0

=>x=-1

17: =>5x-7=2x+2

=>3x=9

=>x=3

16: =>-2x+3+5x-12=0

=>3x-9=0

=>x=3

13: =>-3x+5-2x-11=0

=>-5x-6=0

=>x=-6/5

12: =>4x-9x=15+5

=>-5x=20

=>x=-4

11: =>5x=9

=>x=9/5

10: =>-2x-4x=-5-11

=>-6x=-16

=>x=8/3

\(10,11-2x=4x-5\)

\(\Leftrightarrow-2x-4x=-5-11\)

\(\Leftrightarrow-6x=-16\)

\(\Leftrightarrow x=\dfrac{8}{3}\)

\(11,2x+3=12-3x\)

\(\Leftrightarrow2x+3x=12-3\)

\(\Leftrightarrow5x=9\)

\(\Leftrightarrow x=\dfrac{9}{5}\)

\(12,4x-5=15x+9\)

\(\Leftrightarrow4x-15x=9+5\)

\(\Leftrightarrow-11x=14\)

\(\Leftrightarrow x=-\dfrac{14}{11}\)

\(13,5-3x=11+2x\)

\(\Leftrightarrow-3x-2x=11-5\)

\(\Leftrightarrow-5x=6\)

\(\Leftrightarrow x=-\dfrac{6}{5}\)

\(14,6x+12=3x-5\)

\(\Leftrightarrow6x-3x=-5-12\)

\(\Leftrightarrow3x=-17\)

\(\Leftrightarrow x=-\dfrac{17}{3}\)

\(15,7-3x=9-x\)

\(\Leftrightarrow-3x+x=9-7\)

\(\Leftrightarrow-2x=2\)

\(\Leftrightarrow x=-1\)

\(16,-2x+3=12-5x\)

\(\Leftrightarrow-2x+5x=12-3\)

\(\Leftrightarrow3x=9\)

\(\Leftrightarrow x=3\)

\(17,2\left(x+1\right)=5x-7\)

\(\Leftrightarrow2x+2-5x+7=0\)

\(\Leftrightarrow-3x=-9\)

\(\Leftrightarrow x=3\)

10
`11-2x=4x-5`

`<=>-2x-4x=-5-11`

`<=>-6x=-16`

`<=>x=8/3`

11)

`2x+3=12-3x`

`<=>2x+3x=12-3`

`<=>5x=9`

`<=>x=9/5`

12)

`4x-5=15+9x`

`<=>4x-9x=15+5`

`<=>-5x=20`

`<=>x=-4`

13)

`5-3x=11+2x`

`<=>-3x-2x=11-5`

`<=>-5x=6`

`<=>x=-6/5`

14)

`6x+12=3x-5`

`<=>6x-3x=-5-12`

`<=>3x=-17`

`<=>x=-17/3`

15)

`7-3x=9-x`

`<=>-3x+x=9-7

`<=>-2x=2`

`<=>x=-1`

16)

`-2x+3=12-5x`

`<=>-2x+5x=12-3`

`<=>3x=9`

`<=>x=3`

17)

`2(x+1)=5x-7`

`<=>2x+2=5x-7`

`<=>2x-5x=-7+2`

`<=>-3x=-5`

`<=>x=5/3`