Lời giải:
a.

$x=\frac{-5}{6}-\frac{2}{3}=\frac{-3}{2}$

b.

$\frac{2}{3}x=\frac{1}{10}-\frac{1}{2}=\frac{-2}{5}$

$x=\frac{-2}{5}: \frac{2}{3}=\frac{-3}{5}$

c.

$\frac{7}{8}x=\frac{2}{9}-\frac{1}{3}=\frac{-1}{9}$
$x=\frac{-1}{9}: \frac{7}{8}=\frac{-8}{63}$

d.

$\frac{5}{7}: x=\frac{1}{6}-\frac{4}{5}=\frac{-19}{30}$

$x=\frac{5}{7}: \frac{-19}{30}=\frac{-150}{133}$

e.

$(\frac{2}{5}-1\frac{2}{3}):x=\frac{2}{5}+\frac{3}{5}=1$

$\frac{-19}{15}: x=1$

$x=\frac{-19}{15}:1 =\frac{-19}{15}$

f.

$(-\frac{3}{4}+x).2\frac{2}{3}=1$

$\frac{-3}{4}+x=1: 2\frac{2}{3}=\frac{3}{8}$

$x=\frac{3}{8}+\frac{3}{4}=\frac{9}{8}$

Ta có \(\dfrac{2}{1\cdot5}+\dfrac{2}{5\cdot9}+\dfrac{2}{9\cdot13}+...+\dfrac{2}{x\left(x+4\right)}=\dfrac{56}{113}\)

\(\dfrac{1}{2}\left(\dfrac{4}{1\cdot5}+\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+...+\dfrac{4}{x\left(x+4\right)}\right)=\dfrac{56}{113}\)

\(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{x}-\dfrac{1}{x+4}=\dfrac{56}{113}:\dfrac{1}{2}\)

\(1-\dfrac{1}{x+4}=\dfrac{112}{113}\)

\(\dfrac{1}{x+4}=1-\dfrac{112}{113}=\dfrac{1}{113}\)

x + 4 = 113 ⇒ x = 109

\(\dfrac{2}{1.5}+\dfrac{2}{5.9}+...+\dfrac{2}{x\left(x+4\right)}=\dfrac{56}{113}\)

Xét: \(A=\dfrac{2}{1.5}+\dfrac{2}{5.9}+...+\dfrac{2}{x\left(x+4\right)}\)

\(A=\dfrac{1}{2}.\left(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{x-4}-\dfrac{1}{x}+\dfrac{1}{x}-\dfrac{1}{x+4}\right)\)

\(A=\dfrac{1}{2}.\left(1-\dfrac{1}{x+4}\right)\)

Với \(A=\dfrac{56}{113}\) thì

 \(\dfrac{1}{2}.\left(1-\dfrac{1}{x+4}\right)=\dfrac{56}{113}\)

\(\left(1-\dfrac{1}{x+4}\right)=\dfrac{112}{113}\)

\(\dfrac{1}{x+4}=\dfrac{1}{113}\)

\(x=109\)

\(\dfrac{2}{1.5}\) + \(\dfrac{2}{5.9}\)  + \(\dfrac{2}{9.13}\)+...+  \(\dfrac{2}{x\left(x+4\right)}\)   = \(\dfrac{56}{113}\)

(\(\dfrac{2}{1.5}+\dfrac{2}{5.9}+\dfrac{2}{9.13}+....+\dfrac{2}{x\left(x+4\right)}\) ) \(\times\) 2  = \(\dfrac{56}{113}\) \(\times\) 2

\(\dfrac{4}{1.5}\) + \(\dfrac{4}{5.9}\) +\(\dfrac{4}{9.13}\)+...+ \(\dfrac{4}{x\left(x+4\right)}\)                = \(\dfrac{112}{113}\)

\(\dfrac{1}{1}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{9}\) + \(\dfrac{1}{9}\) - \(\dfrac{1}{13}\) +...+ \(\dfrac{1}{x}\) - \(\dfrac{1}{x+4}\) = \(\dfrac{112}{113}\)

1  - \(\dfrac{1}{x+4}\) = \(\dfrac{112}{113}\)

        \(\dfrac{1}{x+4}\) = 1 - \(\dfrac{112}{113}\)

        \(\dfrac{1}{x+4}\) = \(\dfrac{1}{113}\)

         \(x\) + 4 = 113

         \(x\)        = 113 - 4

         \(x\)        = 109

\(b,\left(2x+1\right).\left(39-2\right)=-55\)

\(\Rightarrow\left(2x+1\right).37=-55\)

\(\Rightarrow3x+1=-\frac{55}{37}\)

\(\Rightarrow3x=-\frac{92}{37}\)

\(\Rightarrow x=-\frac{92}{111}\)

\(c,\left(x-7\right)\left(x+3\right)< 0\)

\(\Rightarrow\orbr{\begin{cases}x-7>0;x+3< 0\\x-7< 0;x+3>0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x>7;x< -3\\x< 7;x>-3\end{cases}}\)

\(\frac{2}{5}.\frac{1}{x}+\frac{1}{x}.2+\frac{2}{5}=0,5\)

\(\Rightarrow\frac{2}{5x}+\frac{2}{x}+\frac{2}{5}=\frac{1}{2}\)

\(\Rightarrow2.\left(\frac{1}{5x}+\frac{1}{x}+\frac{1}{5}\right)=\frac{1}{2}\)

\(\Rightarrow\frac{1}{5x}+\frac{5}{5x}+\frac{x}{5x}=\frac{1}{2}:2=\frac{1}{4}\)

\(\Rightarrow\frac{1+5+x}{5x}=\frac{1}{4}\)

\(\Rightarrow4.\left(1+5+x\right)=5x\)

\(\Rightarrow4+20+4x=5x\)

\(\Rightarrow24+4x=5x\)

\(\Rightarrow5x-4x=24\)

\(\Rightarrow x=24\)

Trả lời

2/5.1/x+1/x.2+2/5=0,5

1/x.(2/5+2)+2/5   =1/2

1/x.12/5+2/5        =1/2

1/x.12/5               =1/2-2/5

1/x.12/5               =1/10

1/x                       =1/10:12/5

1/x                       =1/24.

Hình như mk làm sai !

\(\frac{2}{5}.\frac{1}{x}+\frac{1}{x}.2+\frac{2}{5}=0,5\)

\(\Rightarrow\frac{1}{x}\left(\frac{2}{5}+\frac{4}{2}\right)=\frac{1}{2}-\frac{2}{5}\)

\(\Rightarrow\frac{1}{x}.\frac{12}{5}=\frac{1}{10}\)

\(\Rightarrow\frac{1}{x}=\frac{1}{24}\)

\(\Rightarrow x=24\)

~Study well~

a) 5.(x-20) = 35

(x-20) = 35:5

x-20 = 7

x = 27

b) (x+125) -301 = 56

x+125 -301 = 56

x - 176 = 56

x = 56 +176

x= 232

c) 215 + (x-21):2 = 235

(x-21):2 = 235 - 215

(x-21):2 = 20

x-21 = 20 .2

x-21 = 40

x = 61

d) (x:23 +45) .67 = 8911

(x:23 +45) = 8911 : 67

x:23+45 = 133

x:23 = 133-45

x:23 = 88

x = 88.23

x = 2024

a) 5.(x - 20) = 35

⇒ x - 20 = 35 : 5

⇒ x - 20 = 7

⇒ x = 7 + 20

⇒ x = 27

b) (x + 125) - 301 = 56

⇒ x + 125 = 56 + 301

⇒ x + 125 = 357

⇒ x = 357 - 125

⇒ x = 232

c) 215 + (x - 21) : 2 = 235

⇒ (x - 21) : 2 = 235 - 215

⇒ (x - 21) : 2 = 20

⇒ x - 21 = 20 x 2 

⇒ x - 21 = 40

⇒ x = 21 + 40

⇒ x = 61

d) (x : 23 + 45).67 = 8911

⇒ x : 23 + 45 = 8911 : 67

⇒ x : 23 + 45 = 133

⇒ x : 23 = 133 - 45

⇒ x : 23 = 88

⇒ x = 88 x 23

⇒ x = 2024

a) \(5.\left(x-20\right)=35\)

\(x-20=35:5\)

\(x-20=7\)

\(x=7+20\Rightarrow x=27\)

b) \(\left(x+125\right)-301=56\)

\(x+125=357\)

\(x=357-125\Rightarrow x=232\)

c) \(215+\left(x-21\right):2=235\)

\(\left(x-21\right):2=20\)

\(x-21=40\Rightarrow x=40+21\Rightarrow x=61\)

d) \(\left(x:23+45\right).67=8911\)

\(x:23+45=133\)

\(x:23=88\Rightarrow x=88.23\Rightarrow x=2024\)

a) \(5+3^{x+1}=86\)

\(=>3^{x+1}=86-5\)

\(=>3^{x+1}=81=3^4\)

\(=>x+1=4\) ( cùng cơ số )

\(=>x=4-1\)

\(=>x=3\)

b) \(15:\left(x+2\right)=\left(3^3+3\right):10\)

\(=>15:\left(x+2\right)=\left(27+3\right):10\)

\(=>15:\left(x+2\right)=30:10=3\)

\(=>x+2=15:3\)

\(=>x+2=5\)

\(=>x=5-2\)

\(=>x=3\)

c) \(\left(9x+2\right).4=80\)

\(=>9x+2=80:4\)

\(=>9x+2=20\)

\(=>9x=20-2\)

\(=>9x=18\)

\(=>x=18:9\)

\(=>x=2\)

d) \(\left(245-x\right)+7^2=14\)

\(=>\left(245-x\right)+14=14\)

\(=>245-x=14-14\)

\(=>245-x=0\)

\(=>x=245-0\)

\(=>x=245\)

?

 a, 7x . (x-10 ) = 0

=> \(\hept{\begin{cases}7x=0\\x-10=0\end{cases}}\) => \(\hept{\begin{cases}x=0\\x=10\end{cases}}\)

b,17 . (3x-6).(2x-8) = 0

          (3x-6).(2x-8) = 0 : 17

          (3x-6).(2x-8)  = 0

=>\(\hept{\begin{cases}3x-6=0\\2x-8=0\end{cases}}\)=>\(\hept{\begin{cases}x=2\\x=4\end{cases}}\)

Nhớ nha