Bài 1:

a) \(\dfrac{9}{20}-\dfrac{8}{15}\times\dfrac{5}{12}\)

\(=\dfrac{9}{20}-\dfrac{2}{9}\)

\(=\dfrac{41}{180}\)

b) \(\dfrac{2}{3}\div\dfrac{4}{5}\div\dfrac{7}{12}\)

\(=\dfrac{2}{3}\times\dfrac{5}{4}\times\dfrac{12}{7}\)

\(=\dfrac{5}{6}\times\dfrac{12}{7}\)

\(=\dfrac{10}{7}\)

c) \(\dfrac{7}{9}\times\dfrac{1}{3}+\dfrac{7}{9}\times\dfrac{2}{3}\)

\(=\dfrac{7}{9}\times\left(\dfrac{1}{3}+\dfrac{2}{3}\right)\)

\(=\dfrac{7}{9}\times1\)

\(=\dfrac{7}{9}\)

Bài 2:

a) \(2\times\left(x-1\right)=4026\)

\(\left(x-1\right)=4026\div2\)

\(x-1=2013\)

\(x=2014\)

Vậy: \(x=2014\)

b) \(x\times3,7+6,3\times x=320\)

\(x\times\left(3,7+6,3\right)=320\)

\(x\times10=320\)

\(x=320\div10\)

\(x=32\)

Vậy: \(x=32\)

c) \(0,25\times3< 3< 1,02\)

\(\Leftrightarrow0,75< 3< 1,02\) ( S )

=> \(0,75< 1,02< 3\)

\(a,\dfrac{2}{3}.x=\dfrac{2}{7}\\ x=\dfrac{2}{7}:\dfrac{2}{3}=\dfrac{3}{7}\\ ---\\ b,x.\dfrac{3}{5}=\dfrac{2}{5}\\ x=\dfrac{2}{5}:\dfrac{3}{5}=\dfrac{2}{3}\\ ---\\ c,x:\dfrac{8}{13}=\dfrac{13}{7}\\x=\dfrac{13}{7}.\dfrac{8}{13}=\dfrac{8}{7}\\ ----\\ d,\dfrac{3}{2}:x=\dfrac{7}{4}\\ x=\dfrac{3}{2}:\dfrac{7}{4}=\dfrac{3}{2}.\dfrac{4}{7}=\dfrac{6}{7}\)

a, - \(\dfrac{2}{5}\) + \(\dfrac{4}{5}\).\(x\) = \(\dfrac{3}{5}\)

               \(\dfrac{4}{5}\).\(x\) = \(\dfrac{3}{5}\)+ \(\dfrac{2}{5}\)

                 \(\dfrac{4}{5}\).\(x\) = 1

                      \(x\) = \(\dfrac{5}{4}\)

b, - \(\dfrac{3}{7}\) - \(\dfrac{4}{7}\): \(x\) = \(\dfrac{2}{5}\)

              \(\dfrac{4}{7}\): \(x\) = - \(\dfrac{3}{7}\) - \(\dfrac{2}{5}\)

                \(\dfrac{4}{7}\): \(x\) = - \(\dfrac{29}{35}\)

                  \(x\) = \(\dfrac{4}{7}\): (- \(\dfrac{29}{35}\) )

                  \(x\) = - \(\dfrac{20}{29}\)

c, \(\dfrac{4}{7}\).\(x\) + \(\dfrac{2}{3}\) = - \(\dfrac{1}{5}\)

     \(\dfrac{4}{7}\).\(x\)         = -\(\dfrac{1}{5}\) - \(\dfrac{2}{3}\)

      \(\dfrac{4}{7}\).\(x\)       = - \(\dfrac{13}{15}\)

           \(x\)     = - \(\dfrac{13}{15}\): \(\dfrac{4}{7}\)

            \(x\)    = - \(\dfrac{91}{60}\)

Bài 3:

a: \(S=1+5^2+5^4+\cdots+5^{200}\)

=>25S=\(5^2+5^4+5^6+\cdots+5^{202}\)

=>25S-S=\(5^2+5^4+\cdots+5^{202}-1-5^2-\cdots-5^{200}\)

=>24S=\(5^{202}-1\)

=>\(S=\frac{5^{202}-1}{24}\)

b: \(4^{30}=\left(2^2\right)^{30}=2^{60}=2^{30}\cdot2^{30}=8^{10}\cdot4^{15}\)

\(3\cdot24^{10}=3\cdot3^{10}\cdot8^{10}=8^{10}\cdot3^{11}\)

mà \(4^{15}>3^{11}\)

nên \(4^{30}>3\cdot24^{10}\)

=>\(2^{30}+3^{30}+4^{30}>3\cdot24^{10}\)

Bài 2:

a: |2x-3|>5

=>\(\left[\begin{array}{l}2x-3>5\\ 2x-3<-5\end{array}\right.\Rightarrow\left[\begin{array}{l}2x>8\\ 2x<-2\end{array}\right.\Rightarrow\left[\begin{array}{l}x>4\\ x<-1\end{array}\right.\)

c: |3x-1|<=7

=>-7<=3x-1<=7

=>-6<=3x<=8

=>\(-2\le x\le\frac83\)

d: \(\left|3x-5\right|+\left|2x+3\right|=7\) (1)

TH1: \(x<-\frac32\)

=>2x+3<0; 3x-5<0

(1) sẽ trở thành: -2x-3-3x+5=7

=>-5x+2=7

=>-5x=5

=>x=-1(loại)

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

=>2x+3>=0; 3x-5<0

(1) sẽ trở thành: 2x+3-3x+5=7

=>-x+8=7

=>-x=-1

=>x=-1(nhận)

TH3: x>=5/3

=>2x+3>0; 3x-5>=0

(1) sẽ trở thành: 2x+3+3x-5=7

=>5x-2=7

=>5x=9

=>x=9/5(nhận)

a) 5.2² + (x + 3) = 5²

5.4 + x + 3 = 25

20 + x + 3 = 25

x + 23 = 25

x = 25 - 23

x = 2

b) 2³ + (x - 3²) = 5³ - 4³

8 + (x - 9) = 125 - 64

8 + x - 9 = 61

x - 1 = 61

x = 61 + 1

x = 62

c) 4.(x - 5) - 2³ = 2⁴.3

4x - 20 - 8 = 16.3

4x - 28 = 48

4x = 48 + 28

4x = 76

x = 76 : 4

x = 19

d) 5.(x + 7) - 10 = 2³.5

5x + 35 - 10 = 8.5

5x + 25 = 40

5x = 40 - 25

5x = 15

x = 15 : 5

x = 3

e) 7² - 7.(13 - x) = 14

49 - 91 + 7x = 14

7x - 42 = 14

7x = 14 + 42

7x = 56

x = 56 : 7

x = 8

a) \(5\cdot2^2+\left(x+3\right)=5^2\)

\(\Rightarrow x+3=5^2-5\cdot2^2\)

\(\Rightarrow x+3=25-5\cdot4\)

\(\Rightarrow x+3=5\)

\(\Rightarrow x=5-3\)

\(\Rightarrow x=2\)

b) \(2^3+\left(x-3^2\right)=5^3-4^3\)

\(\Rightarrow8+\left(x-9\right)=125-64\)

\(\Rightarrow8+x-9=61\)

\(\Rightarrow x-1=61\)

\(\Rightarrow x=61+1\)

\(\Rightarrow x=62\)

c) \(4\left(x-5\right)-2^3=2^4\cdot3\)

\(\Rightarrow4\left(x-5\right)=2^4\cdot3+2^3\)

\(\Rightarrow4\cdot\left(x-5\right)=16\cdot3+8\)

\(\Rightarrow4\cdot\left(x-5\right)=56\)

\(\Rightarrow x-5=56:4\)

\(\Rightarrow x-5=14\)

\(\Rightarrow x=19\)

d) \(5\left(x+7\right)-10=2^3\cdot5\)

\(\Rightarrow5\left(x+7\right)=8\cdot5+10\)

\(\Rightarrow5\left(x+7\right)=40+10\)

\(\Rightarrow5\left(x+7\right)=50\)

\(\Rightarrow x+7=10\)

\(\Rightarrow x=10-7\)

\(\Rightarrow x=3\)

e) \(7^2-7\left(13-x\right)=14\)

\(\Rightarrow7\left(13-x\right)=7^2-14\)

\(\Rightarrow7\left(13-x\right)=49-14\)

\(\Rightarrow7\left(13-x\right)=35\)

\(\Rightarrow13-x=5\)

\(\Rightarrow x=13-5\)

\(\Rightarrow x=8\)

f) \(5x-5^2=10\)

\(\Rightarrow5x=10+5^2\)

\(\Rightarrow5x=10+25\)

\(\Rightarrow5x=35\)

\(\Rightarrow x=\dfrac{35}{5}\)

\(\Rightarrow x=7\)

g) \(9x-2\cdot3^2=3^4\)

\(\Rightarrow9x=3^4+2\cdot3^2\)

\(\Rightarrow9x=81+2\cdot9\)

\(\Rightarrow9x=99\)

\(\Rightarrow x=\dfrac{99}{9}\)

\(\Rightarrow x=11\)

h) \(10x+2^2\cdot5=10^2\)

\(\Rightarrow10x=10^2-2^2\cdot5\)

\(\Rightarrow10x=100-4\cdot5\)

\(\Rightarrow10x=80\)

\(\Rightarrow x=\dfrac{80}{10}\)

\(\Rightarrow x=8\)

i) \(125-5\left(4+x\right)=15\)

\(\Rightarrow5\left(4+x\right)=125-5\)

\(\Rightarrow5\left(4+x\right)=120\)

\(\Rightarrow4+x=\dfrac{120}{5}\)

\(\Rightarrow4+x=24\)

\(\Rightarrow x=24-4\)

\(\Rightarrow x=20\)

j) \(2^6+\left(5+x\right)=3^4\)

\(\Rightarrow5+x=3^4-2^6\)

\(\Rightarrow5+x=81-64\)

\(\Rightarrow5+x=17\)

\(\Rightarrow x=17-5\)

\(\Rightarrow x=12\)

giải chi tiết ra giúp mk nhé, cảm ơn nhiều

a,     \(\dfrac{3}{7}\)\(x\)- \(\dfrac{2}{3}\)\(x\)    = \(\dfrac{10}{21}\)

    (\(\dfrac{3}{7}\) - \(\dfrac{2}{3}\)) \(\times\) \(x\)  =  \(\dfrac{10}{21}\)

     - \(\dfrac{5}{21}\) \(\times\) \(x\)      = \(\dfrac{10}{21}\)

                 \(x\)      = \(\dfrac{10}{21}\) : (-\(\dfrac{5}{21}\))

                 \(x\)      = -2 

b, \(\dfrac{7}{35}\) : (\(x-\dfrac{1}{3}\)) = - \(\dfrac{2}{25}\)

            \(x\) - \(\dfrac{1}{3}\)    =  \(\dfrac{7}{35}\) : (- \(\dfrac{2}{25}\))

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

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

              \(x\)      = - \(\dfrac{13}{6}\)

c, 3.(\(x\) - \(\dfrac{1}{2}\)) - 5.(\(x\) + \(\dfrac{3}{5}\)) = - \(x\)+ \(\dfrac{1}{5}\)

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

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

              \(x\)           = - \(\dfrac{47}{10}\)

\(a,\dfrac{3}{7}x-\dfrac{2}{3}x=\dfrac{10}{21}\\ \Rightarrow x\left(\dfrac{3}{7}-\dfrac{2}{3}\right)=\dfrac{10}{21}\\ \Rightarrow x.-\dfrac{5}{21}=\dfrac{10}{21}\\ \Rightarrow x=-2\\ b,\dfrac{7}{35}:\left(x-\dfrac{1}{3}\right)=-\dfrac{2}{25}\\ \Rightarrow\dfrac{1}{5}:\left(x-\dfrac{1}{3}\right)=-\dfrac{2}{25}\\ \Rightarrow x-\dfrac{1}{3}=-\dfrac{5}{2}\\ \Rightarrow x=-\dfrac{13}{6}\\ c,3.\left(x-\dfrac{1}{2}\right)-5.\left(x+\dfrac{3}{5}\right)=-x+\dfrac{1}{5}\\ \Rightarrow3x-\dfrac{3}{2}-5x+5=-x+\dfrac{1}{5}\)

\(\Rightarrow x\left(3-5\right)-\dfrac{3}{2}+5=-x+\dfrac{1}{5}\\ \Rightarrow-2x-\dfrac{13}{2}=-x+\dfrac{1}{5}\\ \Rightarrow-x-\dfrac{13}{5}=\dfrac{1}{5}\\ \Rightarrow x=\dfrac{1}{5}-\dfrac{13}{5}\\ \Rightarrow x=-\dfrac{12}{5}.\)

a: Ta có: \(\dfrac{x+2}{5}=\dfrac{1}{x-2}\)

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

\(\Leftrightarrow x^2=9\)

hay \(x\in\left\{3;-3\right\}\)

b: Ta có: \(\dfrac{x}{x+1}=\dfrac{x+5}{x+7}\)

\(\Leftrightarrow x^2+6x+5=x^2+7x\)

\(\Leftrightarrow6x-7x=-5\)

hay x=5

c: Ta có: \(\dfrac{x-1}{x+2}=\dfrac{x-2}{x+3}\)

\(\Leftrightarrow x^2+2x-3=x^2-4\)

\(\Leftrightarrow2x=-1\)

hay \(x=-\dfrac{1}{2}\)

a) \(\left|\frac{3}{2}x+\frac{1}{2}\right|=\left|4x-1\right|\) 

\(\Rightarrow\orbr{\begin{cases}\frac{3}{2}x+\frac{1}{2}=4x-1\\\frac{3}{2}x+\frac{1}{2}=-4x+1\end{cases}}\Rightarrow\orbr{\begin{cases}4x-\frac{3}{2}x-1=\frac{1}{2}\\-4x-\frac{3}{2}x+1=\frac{1}{2}\end{cases}}\Rightarrow\orbr{\begin{cases}\frac{5}{2}x=\frac{3}{2}\\-\frac{11}{2}x=-\frac{1}{2}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{3}{5}\\x=\frac{1}{11}\end{cases}}\) 

phần b ở đề bài mình ghi sai, là bằng 0 chứ ko phải bằng 10

a, 2/5 + 3/4 : x = -1/2

3/4 : x = -1/2 - 2/5

3/4 : x = -9/10

x = 3/4 : -9/10

x = -5/6

b, 5/7 - 2/3 . x = 4/5 

2/3 . x = 4/5 + 5/7

2/3 . x = 53/35

x = 53/35 : 2/3

x = 159/70