Ta có : 17 - 14(x + 1) = 13 - 4(x + 1) - 5(x - 3)

<=> 17 - 14x - 14 = 13 - 4x - 4 - 5x + 15

<=> -14x + 3 = -9x + 24

<=> -14x + 9x = 24 - 3

<=> -5x = 21

=> x = -4,2

Ta có :  5x + 3,5 + (3x - 4) = 7x - 3(x - 0,5)

<=>  5x + 3,5 + 3x - 4 = 7x - 3x + 1,5 

<=> 8x - 0,5 = 4x + 1,5

=> 8x - 4x = 1,5 + 0,5

=> 4x = 2

=> x = \(\frac{1}{2}\)

17-14(x+1)=13-4(x+1)-5(x-3)

\(a,\dfrac{x-3}{x}=\dfrac{x-3}{x+3}\)\(\left(đk:x\ne0,-3\right)\)

\(\Leftrightarrow\dfrac{x-3}{x}-\dfrac{x-3}{x+3}=0\)

\(\Leftrightarrow\dfrac{\left(x-3\right)\left(x+3\right)-x\left(x-3\right)}{x\left(x+3\right)}=0\)

\(\Leftrightarrow x^2-9-x^2+3x=0\)

\(\Leftrightarrow3x-9=0\)

\(\Leftrightarrow3x=9\)

\(\Leftrightarrow x=3\left(n\right)\)

Vậy \(S=\left\{3\right\}\)

\(b,\dfrac{4x-3}{4}>\dfrac{3x-5}{3}-\dfrac{2x-7}{12}\)

\(\Leftrightarrow\dfrac{4x-3}{4}-\dfrac{3x-5}{3}+\dfrac{2x-7}{12}>0\)

\(\Leftrightarrow\dfrac{3\left(4x-3\right)-4\left(3x-5\right)+2x-7}{12}>0\)

\(\Leftrightarrow12x-9-12x+20+2x-7>0\)

\(\Leftrightarrow2x+4>0\)

\(\Leftrightarrow2x>-4\)

\(\Leftrightarrow x>-2\)

Bài `1:`

`h)(3/4x-1)(5/3x+2)=0`

`=>[(3/4x-1=0),(5/3x+2=0):}=>[(x=4/3),(x=-6/5):}`

______________

Bài `2:`

`b)3x-15=2x(x-5)`

`<=>3(x-5)-2x(x-5)=0`

`<=>(x-5)(3-2x)=0<=>[(x=5),(x=3/2):}`

`d)x(x+6)-7x-42=0`

`<=>x(x+6)-7(x+6)=0`

`<=>(x+6)(x-7)=0<=>[(x=-6),(x=7):}`

`f)x^3-2x^2-(x-2)=0`

`<=>x^2(x-2)-(x-2)=0`

`<=>(x-2)(x^2-1)=0<=>[(x=2),(x^2=1<=>x=+-2):}`

`h)(3x-1)(6x+1)=(x+7)(3x-1)`

`<=>18x^2+3x-6x-1=3x^2-x+21x-7`

`<=>15x^2-23x+6=0<=>15x^2-5x-18x+6=0`

`<=>(3x-1)(5x-1)=0<=>[(x=1/3),(x=1/5):}`

`j)(2x-5)^2-(x+2)^2=0`

`<=>(2x-5-x-2)(2x-5+x+2)=0`

`<=>(x-7)(3x-3)=0<=>[(x=7),(x=1):}`

`w)x^2-x-12=0`

`<=>x^2-4x+3x-12=0`

`<=>(x-4)(x+3)=0<=>[(x=4),(x=-3):}`

`m)(1-x)(5x+3)=(3x-7)(x-1)`

`<=>(1-x)(5x+3)+(1-x)(3x-7)=0`

`<=>(1-x)(5x+3+3x-7)=0`

`<=>(1-x)(8x-4)=0<=>[(x=1),(x=1/2):}`

`p)(2x-1)^2-4=0`

`<=>(2x-1-2)(2x-1+2)=0`

`<=>(2x-3)(2x+1)=0<=>[(x=3/2),(x=-1/2):}`

`r)(2x-1)^2=49`

`<=>(2x-1-7)(2x-1+7)=0`

`<=>(2x-8)(2x+6)=0<=>[(x=4),(x=-3):}`

`t)(5x-3)^2-(4x-7)^2=0`

`<=>(5x-3-4x+7)(5x-3+4x-7)=0`

`<=>(x+4)(9x-10)=0<=>[(x=-4),(x=10/9):}`

`u)x^2-10x+16=0`

`<=>x^2-8x-2x+16=0`

`<=>(x-2)(x-8)=0<=>[(x=2),(x=8):}`

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

\(\Leftrightarrow\left(x-1\right)\left(\left(x-1\right)^2-\left(2x-3\right)\left(3x-5\right)\right)+\left(2x-3\right)\left(\left(2x-3\right)^2-\left(x-1\right)\left(3x-5\right)\right)+\left(3x-5\right)\left(\left(3x-5\right)^2-\left(x-1\right)\left(2x-3\right)\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)\left(7-5x\right)+\left(2x-3\right)\left(x-2\right)^2+\left(3x-5\right)\left(x-2\right)\left(7x-11\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(\left(x-1\right)\left(7-5x\right)+\left(2x-3\right)\left(x-2\right)+\left(3x-5\right)\left(7x-11\right)\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(18x^2-63x+54\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\18x^2-63x+54=0\end{matrix}\right.\)

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

1) Ta có: \(4x+8=3x-1\)

\(\Leftrightarrow4x-3x=-1-8\)

\(\Leftrightarrow x=-9\)

2) Ta có: \(10-5\left(x+3\right)>3\left(x-1\right)\)

\(\Leftrightarrow10-5x-15-3x+3>0\)

\(\Leftrightarrow-8x>2\)

hay \(x< \dfrac{-1}{4}\)

a: =>9x^2+6x+1-6(2x^2-13x+21)=0

=>9x^2+6x+1-12x^2+78x-126=0

=>-3x^2+84x-125=0

=>\(x\in\left\{26.42;1.58\right\}\)

b: =>(3x+1)[(2x-5)^2-(x-3)^2]=0

=>(3x+1)(2x-5-x+3)(2x-5+x-3)=0

=>(3x+1)(x-2)(3x-8)=0

=>\(x\in\left\{-\dfrac{1}{3};2;\dfrac{8}{3}\right\}\)

c; =>(x+5)(0,75x-3+1,25x)=0

=>(x+5)(2x-3)=0

=>x=3/2 hoặc x=-5

+ Với x < - 3, phương trình đã cho có dạng:

( 5 - x ) - ( x + 3 ) = 3x - 1 ⇔ x = 3/5 (loại vì không thỏa mãn điều kiện)

+ Với - 3 ≤ x < 5, phương trình đã cho có dạng:

( 5 - x ) + ( x + 3 ) = 3x - 1 ⇔ 3x = 9 ⇔ x = 3 (thỏa mãn khoảng đang xét)

+ Với x ≥ 5, phương trình đã cho có dạng:

( x - 5 ) + ( x + 3 ) = 3x - 1 ⇔ x = - 1 (không thỏa mãn không xét)

Vậy phương trình đã cho có nghiệm là x = 3

1/ \(2\left(x-5\right)=\left(-x-5\right)\)

\(\Leftrightarrow2x-10=-x-5\)

\(\Leftrightarrow3x=5\)

\(\Leftrightarrow x=\dfrac{5}{3}\)

Vậy: \(S=\left\{\dfrac{5}{3}\right\}\)

==========

2/ \(2\left(x+3\right)-3\left(x-1\right)=2\)

\(\Leftrightarrow2x+6-3x+3=2\)

\(\Leftrightarrow-x=-7\)

\(\Leftrightarrow x=7\)

Vậy: \(S=\left\{7\right\}\)

==========

3/ \(4\left(x-5\right)-\left(3x-1\right)=x-19\)

\(\Leftrightarrow4x-20-3x+1=x-19\)

\(\Leftrightarrow0x=0\)

Vậy: \(S=\left\{x|x\text{ ∈ }R\right\}\) 

===========

4/ \(7-\left(x-2\right)=5\left(2-3x\right)\)

\(\Leftrightarrow7-x+2=10-15x\)

\(\Leftrightarrow14x=1\)

\(\Leftrightarrow x=\dfrac{1}{14}\)

Vậy: \(S=\left\{\dfrac{1}{14}\right\}\)

==========

5/ \(2x-\left(5-3x\right)=7x+1\)

\(\Leftrightarrow2x-5+3x=7x+1\)

\(\Leftrightarrow-2x=6\)

\(\Leftrightarrow x=-3\)

Vậy: \(S=\left\{-3\right\}\)

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Chúc bạn học tốt.

1. \(2\left(x-5\right)=-x-5\)

\(\Leftrightarrow3x=5\)

\(\Leftrightarrow x=\dfrac{5}{3}\)

Vậy \(S=\left\{\dfrac{5}{3}\right\}\)

2. \(2\left(x+3\right)-3\left(x-1\right)=2\)

\(\Leftrightarrow2x+6-3x+3=2\)

\(\Leftrightarrow x=7\)

Vậy \(S=\left\{7\right\}\)

3. \(4\left(x-5\right)-\left(3x-1\right)=x-19\)

\(\Leftrightarrow4x-20-3x+1-x+19=0\)

\(\Leftrightarrow0x=0\)

Vậy \(S=\left\{x\in R\right\}\)

4. \(7-\left(x-2\right)=5\left(2-3x\right)\)

\(\Leftrightarrow7-x+2-10+15x=0\)

\(\Leftrightarrow14x-1=0\)

\(\Leftrightarrow x=\dfrac{1}{14}\)

Vậy \(S=\left\{\dfrac{1}{14}\right\}\)

4. \(2x-\left(5-3x\right)=7x+1\)

\(\Leftrightarrow2x-5+3x-7x-1=0\)

\(\Leftrightarrow-2x-6=0\)

\(\Leftrightarrow x=-3\)

Vậy \(S=\left\{-3\right\}\)

1: Ta có: \(2\left(x-5\right)=\left(-x-5\right)\)

\(\Leftrightarrow2x-10+x+5=0\)

\(\Leftrightarrow3x=5\)

hay \(x=\dfrac{5}{3}\)

2: Ta có: \(2\left(x+3\right)-3\left(x-1\right)=2\)

\(\Leftrightarrow2x+6-3x+3=2\)

\(\Leftrightarrow-x=-7\)

hay x=7

3: Ta có: \(4\left(x-5\right)-\left(3x-1\right)=x-19\)

\(\Leftrightarrow4x-20-3x+1-x+19=0\)

\(\Leftrightarrow0x=0\)(luôn đúng