a) \(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0\)

\(\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)

mà 1/10+1/11+1/12-1/13-1/14 khác 0 nên x+1=0

x=0-1

x=-1

Vậy x=-1

b)(2x-1)⁸=(2x-1)⁶

(2x-1)⁸-(2x-1)⁶=0

(2x-1)⁶[(2x-1)²-1]=0

=> (2x-1)⁶=0    hoặc      (2x-1)²-1=0

     2x-1=0                     (2x-1)²=1

     2x=1                   => 2x-1=1 hoặc 2x-1=-1

     x=1/2                       2x=2            2x=0

                                    x=1              x=0

Vậy x=1/2 hoặc x=1 hoặc x=0

thank bạn Do Le Tu Linh nhìu <3

\(2x+x=\frac{11}{12}\)

\(\Rightarrow x.\left(2+1\right)=\frac{11}{12}\)

\(\Rightarrow x.3=\frac{11}{12}\)

\(\Rightarrow x=\frac{11}{12}:3\)

\(\Rightarrow x=\frac{11}{36}\)

Vậy \(x=\frac{11}{36}\)

Chúc bạn học tốt 

\(2x+x=\frac{11}{12}\)

\(\Leftrightarrow x.\left(2+1\right)=\frac{11}{12}\)

\(\Leftrightarrow x.3=\frac{11}{12}\)

\(\Leftrightarrow x=\frac{11}{12}:3\)

\(\Leftrightarrow x=\frac{11}{12}.\frac{1}{3}\)

\(\Leftrightarrow x=\frac{11}{36}\)

Vậy : \(x=\frac{11}{36}\)

Rất vui vì giúp đc bn !!!

\(2x+x=\frac{11}{12}\)

\(x.\left(2+1\right)=\frac{11}{12}\)

\(x.3=\frac{11}{12}\)

\(x=\frac{11}{12}:3\)

\(x=\frac{11}{36}\)

a) \(\frac{4}{x+5}=\frac{3}{2x-1}\)

=> 4(2x - 1) = 3(x + 5)

=> 8x - 4 = 3x + 15

=> 8x - 3x = 15 + 4

=> 5x = 19

=> x = 19/5

b) \(\frac{x+11}{19}+\frac{x+12}{20}+\frac{x+13}{21}=3\)

=> \(\left(\frac{x+11}{19}-1\right)+\left(\frac{x+12}{20}-1\right)+\left(\frac{x+13}{21}-1\right)=0\)

=> \(\frac{x-8}{19}+\frac{x-8}{20}+\frac{x-8}{21}=0\)

=> \(\left(x-8\right)\left(\frac{1}{19}+\frac{1}{20}+\frac{1}{21}\right)=0\)

=> x - 8 = 0

=> x = 8

c) \(\left(2x-1\right)^2=\left(2x-1\right)^3\)

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

=> \(\left(2x-1\right)^2.\left[1-\left(2x-1\right)\right]=0\)

=> \(\orbr{\begin{cases}\left(2x-1\right)^2=0\\1-\left(2x-1\right)=0\end{cases}}\)

=> \(\orbr{\begin{cases}2x-1=0\\1-2x+1=0\end{cases}}\)

=> \(\orbr{\begin{cases}2x=1\\2-2x=0\end{cases}}\)

=> \(\orbr{\begin{cases}x=\frac{1}{2}\\2x=2\end{cases}}\)

=> \(\orbr{\begin{cases}x=\frac{1}{2}\\x=1\end{cases}}\)

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

<=> 4.(2x - 1) = (x + 3).3

<=> 8x - 4 = 3x + 9

<=> 8x = 3x + 9 + 4

<=> 8x = 3x + 13

<=> 8x - 3x = 13

<=> 5x = 13

<=> x = 13/5

=> x = 13/5

c) (2x - 1)² = (2x - 1)³

<=> 4x² - 4x + 1 = 8x³ - 12x² + 6x - 1

<=> 8x³ - 12x² + 6x - 1 = 4x² - 4x + 1

<=> 8x³ - 12x² + 6x - 1 - 1 = 4x² - 4x

<=> 8x³ - 12x² + 6x - 2x = 4x² - 4x

<=> 8x³ - 12x² + 6x - 2x - 4x = 4x²

<=> 8x³ - 12x² + 10x - 2 = 4x²

<=> 8x³ - 12x² + 10x - 2 - 4x² = 0

<=> 8x² - 16x² + 10x - 2 = 0

<=> 2(x - 1)(2x - 1)² = 0

<=> x - 1 = 0 hoặc 2x - 1 = 0

       x = 0 + 1         2x = 0 + 1

       x = 1               2x = 1

                              x = 1/2

=> x = 1 hoặc x = 1/2

Áp dụng bất đẳng thức AM-GM ta có :

\(B=\frac{12}{x-1}+\frac{x-1+1}{3}=\frac{12}{x-1}+\frac{x-1}{3}+\frac{1}{3}\ge2\sqrt{\frac{12}{x-1}\cdot\frac{x-1}{3}}+\frac{1}{3}=4+\frac{1}{3}=\frac{13}{3}\)

Dấu "=" xảy ra <=> \(\frac{12}{x-1}=\frac{x-1}{3}\Rightarrow x=7\left(x\ge1\right)\). Vậy MinB = 13/3

#)Giải :

a) x + 2x + 3x + ... + 100x = - 213

=> 100x + ( 2 + 3 + 4 + ... + 100 ) = - 213 

=> 100x + 5049 = - 213 

<=> 100x = - 5262

<=> x = - 52,62

#)Giải :

b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}x-\frac{1}{6}\)

\(\Rightarrow\frac{1}{2}x+\frac{1}{4}x=\frac{1}{3}+\frac{1}{6}\)

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

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

\(\Rightarrow\frac{3}{4}x=\frac{1}{2}\)

\(\Leftrightarrow x=\frac{2}{3}\)

a) x + 2x + 3x + ... +100x = -213

=>  x . (1 + 2 + 3 +... + 100) = - 213

=> x . 5050 = -213

=> x           = - 213 : 5050

=> x           = -213/5050

b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}x-\frac{1}{6}\)

=> \(\frac{1}{2}x-\frac{1}{4}x=\frac{1}{3}-\frac{1}{6}\)

=> \(x.\left(\frac{1}{2}-\frac{1}{4}\right)=\frac{1}{6}\)

=> \(x.\frac{1}{4}=\frac{1}{6}\)

=> \(x=\frac{1}{6}:\frac{1}{4}\)

=> \(x=\frac{2}{3}\)

c) 3(x-2) + 2(x-1) = 10

=> 3x - 6 + 2x - 2 = 10

=> 3x + 2x - 6 - 2 = 10

=> 5x - 8 = 10

=> 5x = 10 + 8

=> 5x = 18

=> x = 18:5

=> x = 3,6

d) \(\frac{x+1}{3}=\frac{x-2}{4}\)

=> \(4\left(x+1\right)=3\left(x-2\right)\)

=>\(4x+4=3x-6\)

=> \(4x-3x=-4-6\)

=> \(x=-10\)

b) 2003 - | x - 2003 | = x

=> 2003 - x = | x - 2003 |

=> \(2003-x=\orbr{\begin{cases}x-2003\\2003-x\end{cases}}\)

\(\Rightarrow x=\orbr{\begin{cases}2003-x+2003\\2003-2003+x\end{cases}}\)

\(\Rightarrow x=\orbr{\begin{cases}4006-x\\0+x=x\end{cases}}\)

\(\Rightarrow x=4006-x\)

\(\Rightarrow4006=2x\Rightarrow x=4006:2=2003\)

c) Ta có : \(\left|2x-3\right|\ge0;\left|2x+4\right|\ge0\)

\(\Rightarrow\left|2x-3\right|+\left|2x+4\right|=3-2x+4+2x\)

\(=3+4=7\)

Thay \(\left|2x-3\right|=7\)

\(\Rightarrow2x-3=\orbr{\begin{cases}7\\-7\end{cases}}\Rightarrow2x=\orbr{\begin{cases}10\\-4\end{cases}}\Rightarrow x=\orbr{\begin{cases}5\\-2\end{cases}}\)

Thay \(\left|2x+4\right|=7\)

\(\Rightarrow2x+4=\orbr{\begin{cases}7\\-7\end{cases}}\Rightarrow2x=\orbr{\begin{cases}3\\-11\end{cases}}\Rightarrow x=\orbr{\begin{cases}\frac{3}{2}\\\frac{-11}{2}\end{cases}}\)

Vậy \(x\in\left(5;-2;\frac{3}{2};\frac{-11}{2}\right)\)

\(\frac{x+2}{10^{10}}+\frac{x+2}{11^{11}}=\frac{x+2}{12^{12}}\frac{x+2}{13^{13}}\)

=> x + 2 = 0

=> x       = 0 - 2

=> x       = -2

chuyển vế rồi phân phối, có 1/10^10+...-1/13^13 khác 0

nên x+2=0

rồi tìm x

Tìm x thuộc Z, biết

( 3x+ 4) :( x-3)

x+1 là ước của 2^2+7

Trình bày ra nhé!!

Đỗ Lê Tú Linh giúp mình đi, mình tick cho!!

a)                                                              b)

2x-3=x+1/2                                                    11/12-(2/5+x)=2/3

2x-3-x-1/2=0                                                  11/12-2/5-x=2/3

x-7/2=0                                                         31/60-x=2/3 

x=7/2                                                            x=-3/20

\(a,2x-3=x+\frac{1}{2}\)

\(\Rightarrow2x-x=\frac{1}{2}+3\)

\(\Rightarrow x=\frac{7}{2}\)

\(b,\frac{11}{12}-\left(\frac{2}{5}+x\right)=\frac{2}{3}\)

\(\Rightarrow\frac{11}{12}-\frac{2}{5}-x=\frac{2}{3}\)

\(\Rightarrow x=\frac{11}{12}-\frac{2}{5}-\frac{2}{3}\)

\(\Rightarrow x=\frac{-3}{20}\)