Question

(1,5 điểm) Tìm $x$ biết

a) $\dfrac{3}{4}-\left(x-\dfrac{2}{3}\right)=1 \dfrac{1}{3}$;

b) $\Big| \dfrac{1}{3}-x \Big|=\dfrac{2}{5}$;

c) $\dfrac{x-1}{3}=\dfrac{27}{x-1}$.

Answer 1

3/4 - (x - 2/3) = 1 1/3

3/4 - x + 2/3 = 4/3

-x = 4/3 - 3/4 - 2/3

-x = -1/12

x = 1/12

Answer 2

3/4 - (x - 2/3) = 1 1/3

  3/4 - x + 2/3 = 4/3

         -x = 4/3 - 3/4 - 2/3

         -x = -1/12

          x = 1/12

Answer 3

a) 2 bn làm gòi

b)|1/3-x|=2/5

TH1: 1/3-x=2/5

⇔x=1/3-2/5

⇔x=-1/15

TH2: 1/3-x=-2/5

⇔x=1/3+2/5

⇔x=11/15

Vậy x ϵ {-1/15;11/15}

b)(x-1)/3=27/(x-1)

⇔(x-1)²=3x27

⇔(x-1)²=81

TH1: x-1=9

⇔x=10

TH2:x-1=-9

⇔x=-8

Vậy x ϵ {-8;10}

EZ :>

Answer 4

a)3/4 - (x - 2/3) = 1 1/3

  3/4 - x + 2/3 = 4/3

         -x = 4/3 - 3/4 - 2/3

         -x = -1/12

          x = 1/12

b)|1/3-x|=2/5

TH1: 1/3-x=2/5

⇔x=1/3-2/5

⇔x=-1/15

TH2: 1/3-x=-2/5

⇔x=1/3+2/5

⇔x=11/15

Vậy x ϵ {-1/15;11/15}
c)

(x-1)/3=27/(x-1)

⇔(x-1)2=3x27

⇔(x-1)2=81

TH1: x-1=9

⇔x=10

TH2:x-1=-9

⇔x=-8

Vậy x ϵ {-8;10}

Answer 5

a)3/4 - (x - 2/3) = 1 1/3

  3/4 - x + 2/3 = 4/3

         -x = 4/3 - 3/4 - 2/3

         -x = -1/12

          x = 1/12

b)|1/3-x|=2/5

TH1: 1/3-x=2/5

⇔x=1/3-2/5

⇔x=-1/15

TH2: 1/3-x=-2/5

⇔x=1/3+2/5

⇔x=11/15

Vậy x ϵ {-1/15;11/15}
c)

(x-1)/3=27/(x-1)

⇔(x-1)2=3x27

⇔(x-1)2=81

TH1: x-1=9

⇔x=10

TH2:x-1=-9

⇔x=-8

Vậy x ϵ {-8;10}

Answer 6

a) x=1/12  b)x€{-1/15;11/15} c=10;-8

Answer 7

a)3/4-(x-2/3)=4/3

(x-2/3)=3/4-4/3

x-2/3=-7/12

x=-7/12+2/3

x=1/12

b)[1/3-x]=2/5

Th1:1/3-x=-2/5

x=1/3--2/5

x=1/3+2/5

x=11/15

Th2:1/3-x=2/5

x=1/3-2/5

x=-1/15

c)x-1/3=27/x-1

(x-1)²=3.27

(x-1)²=81

Th1:

x-1=9

x=9+1

x=10

Th2:

x-1=-9

x=-9-1

x=-10

Answer 8

a) 3/4 - (x - 2/3) = 1 1/3

3/4 - x + 2/3 = 4/3

-x = 4/3 - 3/4 - 2/3

-x = -1/12

x = 1/12

b)|1/3-x|=2/5

TH1: 1/3-x=2/5

⇔x=1/3-2/5

⇔x=-1/15

TH2: 1/3-x=-2/5

⇔x=1/3+2/5

⇔x=11/15

Vậy x ϵ {-1/15;11/15}

c)(x-1)/3=27/(x-1)

⇔(x-1)2=3x27

⇔(x-1)2=81

TH1: x-1=9

⇔x=10

TH2:x-1=-9

⇔x=-8

Vậy x ϵ {-8;10}

Answer 9

a) \(\dfrac{3}{4}-\left(x-\dfrac{2}{3}\right)=1\dfrac{1}{3}\)

\(\dfrac{3}{4}-\left(x-\dfrac{2}{3}\right)=\dfrac{4}{3}\)

\(x-\dfrac{2}{3}=\dfrac{3}{4}-\dfrac{4}{3}\)

\(x-\dfrac{2}{3}=\dfrac{-7}{12}\)

\(x=\dfrac{-7}{12}+\dfrac{2}{3}\)

\(x=\dfrac{-7+8}{12}\)

\(x=\dfrac{1}{12}\)

b) \(\left|\dfrac{1}{3}-x\right|=\dfrac{2}{5}\)

\(\left|-\dfrac{2}{5}\right|=\dfrac{2}{5}\)

\(\left|\dfrac{2}{5}\right|=\dfrac{2}{5}\)

=> \(\dfrac{1}{3}-x=\dfrac{2}{5}\)

=> \(\dfrac{1}{3}-x=\dfrac{-2}{5}\)

TH1: \(\dfrac{1}{3}-x=\dfrac{2}{5}\)

\(x=\dfrac{1}{3}-\dfrac{2}{5}\)

\(x=\dfrac{-1}{15}\)

TH2: \(\dfrac{1}{3}-x=\dfrac{-2}{5}\)

\(x=\dfrac{1}{3}+\dfrac{2}{5}\)

\(x=\dfrac{11}{15}\)

c) \(\dfrac{x-1}{3}=\dfrac{27}{x-1}\)

\(\left(x-1\right)\left(x-1\right)=3\cdot27\)

\(\left(x-1\right)^2=81\)

\(\left(x-1\right)^2=9^2=\left(-9\right)^2\)

TH1: x-1 = 9

x = 10

TH2: x-1 = -9

x = -9 +1

x= -8

Vậy x ϵ { 10 ; -8}

Answer 10

a) 3/4 - (x - 2/3) = 1\(\dfrac{1}{3}\)

3/4 - (x - 2/3) = 4/3

x - 2/3 = 3/4 - 4/3

x - 2/3 = -7/12

x = -7/12 + 2/3

x = 1/12

b)|1/3 - x| = 2/5

|-2/5| = 2/5

|2/5| = 2/5

=> 1/3 - x = 2/5

=> 1/3 -x = -2/5

TH1: 1/3 - x = 2/5

x = 1/3 - 2/5

x = -1/15

TH2: 1/3 - x = -2/5

x = 1/3 + 2/5

x = 11/15

c) (x-1)(x-1) = 3.27

(x-1)² = 81

(x-1)²  = 9² = (-9)²

TH1: x - 1 = 9

 x = 10 

TH2: x - 1 = -9

x  = -8

 

Answer 11

a) 3/4 - (x - 2/3) = 1 1/3                 b) | 1/3 - x | = 2/5          c)x - 1/3 = 27/x - 1

            (x - 2/3) = 3/4 - 1 1/3         1/3 - x = -2/5                áp dụng tính chất tỉ lệ thức, 

             x - 2/3  = -7/12                 hoặc 1/3 - x = 2/5         ta được:

             x          = - 7/12 + 2/3       x = 11/15                      ( x - 1)^2 =3,27

             x          =  1/12               hoặc x = -1/15.               ( x - 1)^2 = 81

                                                                                          x -1 = 9 hoặc x -1 = -9

                                                                                          x = 10 hoặc x = -8

Answer 12

3/4 - (x - 2/3) = 1 1/3

3/4 - x + 2/3 = 4/3

3/4 - x = 4/3 - 2/3

3/4 - x = 2/3

x = 9/12 - 8/12

x = 1/12

b)|1/3-x|=2/5

TH1: 1/3-x=2/5

⇔x=1/3-2/5

⇔x=-1/15

TH2: 1/3-x=-2/5

⇔x=1/3+2/5

⇔x=11/15

Vậy x ϵ {-1/15;11/15}

c)(x-1)/3=27/(x-1)

=>(x-1)^2=3x27

=>(x-1)^2=81

TH1: x-1=9

=>x=10

TH2:x-1=-9

=>x= -8

Vậy x thuộc {-8;10}

 

Answer 13

3/4 - (x - 2/3) = 1 1/3

3/4 - x + 2/3 = 4/3

3/4 - x = 4/3 - 2/3

3/4 - x = 2/3

x = 9/12 - 8/12

x = 1/12

b)|1/3-x|=2/5

TH1: 1/3-x=2/5

⇔x=1/3-2/5

⇔x=-1/15

TH2: 1/3-x=-2/5

⇔x=1/3+2/5

⇔x=11/15

Vậy x ϵ {-1/15;11/15}

c)(x-1)/3=27/(x-1)

=>(x-1)^2=3x27

=>(x-1)^2=81

TH1: x-1=9

=>x=10

TH2:x-1=-9

=>x= -8

Vậy x thuộc {-8;10}

 

Answer 14

a.x= 1/12

b.x thuộc {11/15;-11/15}

c.x thuộc {8;-10}

Answer 15

a)1/12

b)-1/15 , 11/15

c)10,-8

Answer 16

a, x=1/12

b, x=-1/15 và11/15

c, x=82 và 80