\(3< \left|3+2x\right|< 4\)

\(\Leftrightarrow\orbr{\begin{cases}3< 3+2x< 4\\-3>3+2x>-4\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}0< 2x< 1\\-6>2x>-7\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}0< x< \frac{1}{2}\\-3>x>\frac{-7}{2}\end{cases}}\)

\(B=\left(1-\frac{3}{2.4}\right)\left(1-\frac{3}{3.5}\right)\left(1-\frac{3}{4.6}\right)...\left(1-\frac{3}{n\left(n+2\right)}\right)\)

\(=\frac{1.5}{2.4}.\frac{2.6}{3.5}.\frac{3.7}{4.6}...\frac{\left(n-1\right)\left(n+3\right)}{n\left(n+2\right)}\)

\(=\frac{\left[1.2.3...\left(n-1\right)\right]\left[5.6.7...\left(n+3\right)\right]}{\left(2.3.4...n\right)\left[4.5.6...\left(n+2\right)\right]}\)

\(=\frac{n+3}{4n}< 2\left(đpcm\right)\)

75=75¹

75 = \(\varnothing\)

Hoặc 

75 = \(\sqrt{75}\)

75 = - \(\sqrt{75}\)

Ta có : \(\frac{b}{a}=2\Leftrightarrow b=2a\)và \(\frac{c}{b}=3\Leftrightarrow c=3b=3\cdot2a=6a\)

Do đó \(\frac{a+b}{b+c}=\frac{a+2a}{2a+6a}=\frac{3a}{8a}=\frac{3}{8}\)

Vậy \(\frac{a+b}{b+c}=\frac{3}{8}\)

Thêm đk \(a,b,c\ne0\)

Ta có: \(\frac{ab}{a+b}=\frac{1}{3}\Rightarrow\frac{a+b}{ab}=3\)

\(\frac{bc}{b+c}=\frac{1}{4}\Rightarrow\frac{bc}{b+c}=4\)

\(\frac{ca}{c+a}=\frac{1}{5}\Rightarrow\frac{c+a}{ca}=5\)

\(\Rightarrow\frac{a+b}{ab}+\frac{b+c}{bc}+\frac{c+a}{ca}=12\)

\(\Leftrightarrow\frac{1}{b}+\frac{1}{a}+\frac{1}{c}+\frac{1}{b}+\frac{1}{a}+\frac{1}{c}=12\)

\(\Leftrightarrow2\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)=12\)

\(\Leftrightarrow\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=6\)

a) x/5 >2

    x/5>10/5

=>x>10

=> x \(\in\){ 11;12;13;14;15;16;.....}

c) x/-4<2

x/-4<-8/-4

=>x<-8

=> x\(\in\){-9;-10;-11;-12;-13;-14;-15;-16;-17;-18;....}

m ko biết làm câu b

a) 

x/5 >2 

(=) x/5 -2 >0

(=) (x-10)/5 >0 

(=) x-10>0

(=) x>10

b)

-5<0 

=> -5/x <0 

(=) x>0

c)

x/-4 <2

(=) -x/4 - 2<0

(=) (-x-8)/4 <0

(=) -x-8<0

(=) -x<8

(=) x>-8

Ghép cặp các số hạng lại thôi

\(P=d\left(a+b\right)+c\left(a+b\right)=\left(a+b\right)\left(c+d\right)=67.30=2010\)

Biết rằng t/x =4/3, y/z =3/2 , z/x =1/6 , hãy tìm tỉ số t/y là đúng nhé

\(\frac{t}{x}=\frac{4}{3},\frac{y}{z}=\frac{3}{2},\frac{z}{y}=\frac{1}{6}(gt)\)

Mặt khác \(\frac{t}{y}=\frac{t}{x}\cdot\frac{x}{z}\cdot\frac{z}{y}=\frac{4}{3}\cdot\frac{6}{1}\cdot\frac{2}{3}=\frac{16}{3}\)

Vậy : ...

a)x/-15=-60/x

<=> x.x=-15.(-60)

         2x=900

           x=900:2

           x=450

vậy x=450

b) -2/x=-x/8

     x.(-x)=-2.8

      -2x=-16

         x=-16:(-2)

         x=8

vậy x=8

a) Ta có: x /-15 = -60/x <=> (-15)(-60)= x.x

<=> 900= x^2 => x= -30; 30

b) Ta có :  (-2)*8 = x*(-x)

<=> -16= x*(-x) <=> 16= x^2 

=> x=  -4; 4