a. \(\frac{1}{5}=0,2\)

\(\Rightarrow|x|=-0,2\)

b.\(\frac{x+9}{15}=\frac{3}{5}\)

\(\frac{9}{15}=\frac{3}{5}\Rightarrow\frac{x+9}{15}=\frac{9}{5}\)

\(\Rightarrow x=0\)

c. \(|x|=0,75=\frac{3}{4}\)

\(|x|=\frac{3}{4}\)

\(|x|=-0,75\)

d.\(\frac{x}{169}=\frac{10^4}{x}\)

\(\frac{x}{169}=\frac{10000}{x}\)

\(\Rightarrow x=-1300\)

\(a.\)

\(\dfrac{1}{3}\left(\dfrac{1}{2}-6\right)+5x=x-\dfrac{3}{5}\)

\(\Rightarrow\dfrac{1}{6}-2+5x=x-\dfrac{3}{5}\)

\(\Rightarrow\dfrac{1}{6}-2+\dfrac{3}{5}=-5x+x\)

\(\Rightarrow-4x=-\dfrac{37}{30}\)

\(\Rightarrow4x=\dfrac{37}{30}\)

\(\Rightarrow x=\dfrac{37}{120}\)

\(b.\)

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

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

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

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

\(\Rightarrow x=\dfrac{3}{2}\)

\(c.\)

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

\(\Rightarrow x+\dfrac{3}{4}x=\dfrac{1}{3}+\dfrac{5}{4}\)

\(\Rightarrow\dfrac{7}{4}x=\dfrac{19}{12}\)

\(\Rightarrow x=\dfrac{19}{21}\)

\(d.\)

\(\dfrac{3}{2}\left(x-\dfrac{5}{3}\right)-\dfrac{7}{5}=x+1\)

\(\Rightarrow\dfrac{3}{2}x-\dfrac{5}{2}-\dfrac{7}{5}=x+1\)

\(\Rightarrow\dfrac{3}{2}x-\dfrac{39}{10}=x+1\)

\(\Rightarrow\dfrac{3}{2}x-x=\dfrac{39}{10}+1\)

\(\Rightarrow\dfrac{1}{2}x=\dfrac{49}{10}\)

\(\Rightarrow x=\dfrac{49}{5}\)

\(e.\)

\(\dfrac{2}{3}\left|4x+3\right|=\dfrac{6}{15}\)

\(\Rightarrow\left|4x+3\right|=\dfrac{3}{5}\)

\(\Rightarrow\left[{}\begin{matrix}4x+3=\dfrac{3}{5}\\4x+3=-\dfrac{3}{5}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}4x=-\dfrac{12}{5}\\4x=-\dfrac{18}{5}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{3}{5}\\x=-\dfrac{9}{10}\end{matrix}\right.\)

a) \(\dfrac{1}{3}.\left(\dfrac{1}{2}-6\right)+5x=x-\dfrac{3}{5}\Leftrightarrow\dfrac{1}{6}-2+5x=x-\dfrac{3}{5}\)

\(\Leftrightarrow5x-x=-\dfrac{3}{5}-\dfrac{1}{6}+2\Leftrightarrow4x=\dfrac{37}{30}\Leftrightarrow x=\dfrac{\dfrac{37}{30}}{4}=\dfrac{37}{120}\)

vậy \(x=\dfrac{37}{120}\)

b) \(\dfrac{3}{2}x-1\dfrac{1}{2}=x-\dfrac{3}{4}\Leftrightarrow\dfrac{3}{2}x-x=\dfrac{-3}{4}+1\dfrac{1}{2}\Leftrightarrow\dfrac{1}{2}x=\dfrac{-3}{4}+\dfrac{3}{2}\)

\(\Leftrightarrow\dfrac{1}{2}x=\dfrac{3}{4}\Leftrightarrow x=\dfrac{3}{4}.2=\dfrac{6}{4}=\dfrac{3}{2}\) vậy \(x=\dfrac{3}{2}\)

c) \(x-\dfrac{5}{4}=\dfrac{1}{3}-\dfrac{3}{4}x\Leftrightarrow x+\dfrac{3}{4}x=\dfrac{1}{3}+\dfrac{5}{4}\Leftrightarrow\dfrac{7}{4}x=\dfrac{19}{12}\)

\(\Leftrightarrow x=\dfrac{\dfrac{19}{12}}{\dfrac{7}{4}}=\dfrac{19}{21}\) vậy \(x=\dfrac{19}{21}\)

d) \(\dfrac{3}{2}\left(x-\dfrac{5}{3}\right)-\dfrac{7}{5}=x+1\Leftrightarrow\dfrac{3}{2}x-\dfrac{5}{2}-\dfrac{7}{5}=x+1\)

\(\Leftrightarrow\dfrac{3}{2}x-x=1+\dfrac{5}{2}+\dfrac{7}{5}\Leftrightarrow\dfrac{1}{2}x=\dfrac{49}{10}\Leftrightarrow x=\dfrac{49}{10}.2=\dfrac{49}{5}\)

vậy \(x=\dfrac{49}{5}\)

e) \(\dfrac{2}{3}\left|4x+3\right|=\dfrac{6}{15}\Leftrightarrow\left|4x+3\right|=\dfrac{\dfrac{6}{15}}{\dfrac{2}{3}}=\dfrac{3}{5}\)

th1 : \(4x+3\ge0\Leftrightarrow4x\ge-3\Leftrightarrow x\ge\dfrac{-3}{4}\)

\(\Rightarrow\left|4x+3\right|=\dfrac{3}{5}\Leftrightarrow4x+3=\dfrac{3}{5}\Leftrightarrow4x=\dfrac{3}{5}-3=\dfrac{-12}{5}\)

\(\Leftrightarrow x=\dfrac{\dfrac{-12}{5}}{4}=\dfrac{-3}{5}\left(tmđk\right)\)

th2: \(4x+3< 0\Leftrightarrow4x< -3\Leftrightarrow x< \dfrac{-3}{4}\)

\(\Rightarrow\left|4x+3\right|=\dfrac{3}{5}\Leftrightarrow-\left(4x+3\right)=\dfrac{3}{5}\Leftrightarrow-4x-3=\dfrac{3}{5}\)

\(\Leftrightarrow4x=-3-\dfrac{3}{5}=\dfrac{-18}{5}\Leftrightarrow x=\dfrac{\dfrac{-18}{5}}{4}=\dfrac{-9}{10}\left(tmđk\right)\)

vậy \(x=\dfrac{-3}{5};x=\dfrac{-9}{10}\)

a) \(\frac{9}{20}\)                                                   c) \(\frac{-55}{4}\)                                                                                                                                 

b) \(\frac{116}{75}\)                                                d) \(\frac{-76}{45}\)

đúng hết đấy nhé mình tính kĩ lắm ko sai đâu

       chúc may mắn

|\(\frac32x\) + \(\frac12\)| = |4\(x\) - 1|

\(\left[\begin{array}{l}\frac32x+\frac12=-4x+1\\ \frac32x+\frac12=4x-1\end{array}\right.\)

\(\left[\begin{array}{l}\frac32x+4x=1-\frac12\\ \frac32x-4x=-1-\frac12\end{array}\right.\)

\(\left[\begin{array}{l}\frac{11}{2}x=\frac12\\ -\frac52x=-\frac32\end{array}\right.\)

\(\left[\begin{array}{l}x=\frac12:\frac{11}{2}\\ x=-\frac32:\frac{-5}{2}\end{array}\right.\)

\(\left[\begin{array}{l}x=\frac12\times\frac{2}{11}\\ x=-\frac32\times\frac{-2}{5}\end{array}\right.\)

\(\left[\begin{array}{l}x=\frac{1}{11}\\ x=\frac35\end{array}\right.\)

Vậy \(x\in\) {\(\frac{1}{11};\frac35\)}

|\(\frac54x\) - \(\frac72\)| - |\(\frac58x\) + \(\frac35\)| = 0

|\(\frac54x\) - \(\frac72\)| = |\(\frac58x\) + \(\frac35\)|

\(\left[\begin{array}{l}\frac54x-\frac72=-\frac58x-\frac35\\ \frac54x-\frac72=\frac58x+\frac35\end{array}\right.\)

\(\left[\begin{array}{l}\frac54x+\frac58x=\frac72-\frac35\\ \frac54x-\frac58x=\frac72+\frac35\end{array}\right.\)

\(\left[\begin{array}{l}\frac{15}{8}x=\frac{29}{20}\\ \frac58x=\frac{41}{10}\end{array}\right.\)

\(\left[\begin{array}{l}x=\frac{29}{10}:\frac{15}{8}\\ x=\frac{41}{10}:\frac58\end{array}\right.\)

\(\left[\begin{array}{l}x=\frac{116}{75}\\ x=\frac{164}{25}\end{array}\right.\)

Vậy \(x\in\) {\(\frac{116}{75}\); \(\frac{164}{25}\)}

Câu a:

18 - |x - 1| = 2^2

18 - |x - 1| = 4

|x - 1| = 18 - 4

|x - 1| = 14

x - 1 = -14 hoặc x - 1 = 14

Th1: x - 1 = -14

x = - 14 + 1

x = -13

Th2: x - 1 = 14

x = 14 + 1

x = 15

Vậy x ∈ {-13; 15}

Câu b:

x - {55 - [49 + (-28 - x)]} = 13 - {47 + [25 - (32 - x)]}

x - {55 - [49 - 28 - x]} = 13 - {47 + [25 - 32 + x]}

x - {55 - 49 + 28 + x} = 13 - {47 + 25 - 32 + x}

x - {6 + 28 + x} = 13 - {72 - 32 + x}

x - {34 + x} = 13 - {40 + x}

x - 34 - x = 13 - 40 - x

(x - x) + x = 13 - 40 + 34

0 + x = - 27 + 34

x = 7

Vậy x = 7

a,10

b,6

làm được hai câu thông cảm

dài :vv

a) \(\left|2x-5\right|=4\Leftrightarrow\hept{\begin{cases}2x-5=4\\2x-5=-4\end{cases}\Leftrightarrow\hept{\begin{cases}2x=9\\2x=1\end{cases}\Leftrightarrow}\hept{\begin{cases}x=\frac{9}{2}\\x=\frac{1}{2}\end{cases}}}\)

b) \(\frac{1}{3}-\left|\frac{5}{4}-2x\right|=\frac{1}{4}\)

\(\Leftrightarrow\left|\frac{5}{4}-2x\right|=\frac{1}{12}\Leftrightarrow\hept{\begin{cases}\frac{5}{4}-2x=\frac{1}{12}\\\frac{5}{4}-2x=-\frac{1}{12}\end{cases}\Leftrightarrow\hept{\begin{cases}2x=\frac{7}{6}\\2x=\frac{4}{3}\end{cases}}\Leftrightarrow\hept{\begin{cases}x=\frac{7}{12}\\x=\frac{2}{3}\end{cases}}}\)

Bài 1 :

a) \(|2x-5|=4\)

\(\Rightarrow\orbr{\begin{cases}2x-5=4\\2x-5=-4\end{cases}\Rightarrow}\orbr{\begin{cases}2x=9\\2x=1\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{9}{2}\\x=\frac{1}{2}\end{cases}}}\)

b) \(\frac{1}{3}-\left|\frac{5}{4}-2x\right|=\frac{1}{4}\)

\(\Rightarrow\left|\frac{5}{4}-2x\right|=\frac{1}{12}\)

\(\Rightarrow\orbr{\begin{cases}\frac{5}{4}-2x=\frac{1}{12}\\\frac{5}{4}-2x=-\frac{1}{12}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}2x=\frac{7}{6}\\2x=\frac{4}{3}\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{7}{12}\\x=\frac{2}{3}\end{cases}}}\)

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

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

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

\(\Rightarrow\left|x-\frac{1}{3}\right|=0\Rightarrow x-\frac{1}{3}=0\Rightarrow x=\frac{1}{3}\)

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

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

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

Vì \(\left|x\right|\ge0\Rightarrow\)ko có gtri nào của x thỏa mãn đề bài

Bài 2 :

a) \(\left|x-1\right|=3x+2\)

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

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

b|) \(\left|9+x\right|=2x\Rightarrow\orbr{\begin{cases}9+x=2x\\9+x=-2x\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x-2x=-9\\x+2x=-9\end{cases}\Rightarrow\orbr{\begin{cases}-x=-9\\3x=-9\end{cases}\Rightarrow}\orbr{\begin{cases}x=9\\x=-3\end{cases}}}\)

c) \(\left|x+6\right|-9=2x\Rightarrow\left|x+6\right|=2x+9\)

\(\Rightarrow\orbr{\begin{cases}x+6=2x+9\\x+6=-2x-9\end{cases}\Rightarrow}\orbr{\begin{cases}x-2x=9-6\\x+2x=-9-6\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}-x=3\\3x=-15\end{cases}\Rightarrow\orbr{\begin{cases}x=-3\\x=-5\end{cases}}}\)

Cậu có thể tham khảo bài làm trên đây ạ, chúc cậu học tốt ^^

Bài 2  :x+1/3=x-3/4                                  <=>4.(x+1)=3.(x-3)                             4x+4=3x-9                                                   4x-3x=-9-4                                                    x=-13

Bài 1: 

ta có: \(\frac{17}{x+1}.\frac{x}{6}=\frac{17x}{6x+6}\)

Để 17x/6x+6 thuộc Z

=> 17x chia hết cho 6x + 6

=> 102x chia hết cho 6x + 6

102x + 102 - 102 chia hết cho 6x + 6

17.(6x+6) - 102 chia hết cho 6x+6

mà 17.(6x+6) chia hết cho 6x + 6

=> 102 chia hết cho 6x + 6

=> ...

bn tự lm típ nha!

Bài 2:

ta có: \(\frac{x+1}{3}=\frac{x-3}{4}\)

\(\Rightarrow4x+4=3x-9\)

\(\Rightarrow4x-3x=-9-4\)

\(x=-13\)