a, 3/5 + x = 1/2 + 1

    3/5 + x = 3/2

             x  = 3/2 - 3/5

             x =      9/10

a)3/2-3/5

=15-10-6/10

=9/10

b)3:X=2/3+5/2

3:X=4/6+15/6

3:X=19/6

X=3:19/6

X=19/18

a) \(\dfrac{3}{5}+x=\dfrac{1}{2}+1\)

     \(\dfrac{3}{5}+x=\dfrac{3}{2}\) 

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

            \(x=\dfrac{15}{10}-\dfrac{6}{10}\)

            \(x=\dfrac{9}{10}\)

b) \(3:x=\dfrac{2}{3}+2\dfrac{1}{2}\)

    \(3:x=\dfrac{2}{3}+\dfrac{5}{2}\)

    \(3:x=\dfrac{4}{6}+\dfrac{15}{6}\)

    \(3:x=\dfrac{19}{6}\)

         \(x=3:\dfrac{19}{6}\)

         \(x=\dfrac{18}{19}\)

a)

\(\left|x-2\right|-\dfrac{3}{5}=\dfrac{1}{2}\\ \left|x-2\right|=\dfrac{1}{2}+\dfrac{3}{5}\\ \left|x-2\right|=\dfrac{11}{10}\\ =>\left[{}\begin{matrix}x-2=\dfrac{11}{10}\\x-2=-\dfrac{11}{10}\end{matrix}\right.\left[{}\begin{matrix}x=\dfrac{31}{10}\\x=\dfrac{9}{10}\end{matrix}\right.\)

b)

\(\left(x-\dfrac{7}{3}\right):\dfrac{-1}{3}=0,4\\ x-\dfrac{7}{3}=0,4\cdot\dfrac{-1}{3}\\ x-\dfrac{7}{3}=-\dfrac{2}{15}\\ x=-\dfrac{2}{15}+\dfrac{7}{3}\\ x=\dfrac{11}{5}\)

c)

\(\left|x-3\right|=5\\ =>\left[{}\begin{matrix}x-3=5\\x-3=-5\end{matrix}\right.\left[{}\begin{matrix}x=5+3\\x=-5+3\end{matrix}\right.\left[{}\begin{matrix}x=8\\x=-2\end{matrix}\right.\)

d)

\(\left(2x+3\right)^2=25\\ =>\left[{}\begin{matrix}2x+3=5\\2x+3=-5\end{matrix}\right.\left[{}\begin{matrix}2x=2\\2x=-8\end{matrix}\right.\left[{}\begin{matrix}x=1\\x=-4\end{matrix}\right.\)

e)

\(\dfrac{3}{4}+\dfrac{1}{4}:x=\dfrac{2}{5}\)

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

\(\dfrac{1}{4}:x=-\dfrac{7}{20}\)

\(x=\dfrac{1}{4}:\dfrac{-7}{20}\\ x=-\dfrac{5}{7}\)

f)

\(\left(x-\dfrac{1}{2}\right)^3=\dfrac{1}{27}\\ =>x-\dfrac{1}{2}=\dfrac{1}{3}\\ x=\dfrac{1}{3}+\dfrac{1}{2}\\ x=\dfrac{5}{6}\)

a) \(\dfrac{4}{5}\left(x-\dfrac{1}{3}\right)-3\dfrac{1}{2}=50\%\)

\(\dfrac{4}{5}x-\dfrac{4}{15}-\dfrac{7}{2}=\dfrac{1}{2}\)

\(\dfrac{4}{5}x=\dfrac{1}{2}+\dfrac{7}{2}+\dfrac{4}{15}\)

\(\dfrac{4}{5}x=\dfrac{64}{15}\)

\(x=\dfrac{64}{15}:\dfrac{4}{5}\\ x=\dfrac{16}{3}\)

b) \(8\dfrac{3}{5}.x-2\dfrac{1}{5}.x=16\%\)

\(\dfrac{43}{5}x-\dfrac{11}{5}x=\dfrac{4}{25}\)

\(\dfrac{32}{5}x=\dfrac{4}{25}\)

\(x=\dfrac{4}{25}:\dfrac{32}{5}\)

\(x=\dfrac{1}{40}\)

a: =>x=2/3-3/4=8/12-9/12=-1/12

b: =>|x-2/3|=4/5+1/2=8/10+5/10=13/10

=>x-2/3=13/10 hoặc x-2/3=-13/10

=>x=59/30 hoặc x=-19/30

a:

x = 2/3 - 3/4

x =... (tự tính)

B:

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

x - 2/3 = 13/10

x = 13/10 + 2/3

X=... (tự tính)

2/10 = 1/5

=> x = 1

3/5 x  = 1/4 + 1/3

3/5x = 7/12

x = 7/12 : 3/5

x = 35/36

1/5: x = 2/35

x = 1/5 : 2/35

x = 7/2

\(\dfrac{x}{5}=\dfrac{2}{10}\)

=> \(\dfrac{x}{5}=\dfrac{1}{5}\)

=> x=1

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

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

=>\(\dfrac{3}{5}x=\dfrac{7}{12}\)

=>   \(x=\dfrac{7}{12}:\dfrac{3}{5}\)

=>   x = \(\dfrac{35}{36}\)

\(\dfrac{1}{5}:x=\dfrac{1}{5}-\dfrac{1}{7}\)

=>\(\dfrac{1}{5}:x=\dfrac{2}{35}\)

=>        \(x=\dfrac{1}{5}:\dfrac{2}{35}\)

=>        \(x=\dfrac{7}{2}\)

\(a.x=\dfrac{5.2}{10}=1\\ b.x=\dfrac{3}{5}x=\dfrac{1}{4}+\dfrac{1}{3}=\dfrac{7}{12}\\ x=\dfrac{7}{12}:\dfrac{3}{5}=\dfrac{7}{12}.\dfrac{5}{3}=\dfrac{35}{36}\\ c.\dfrac{1}{5}:x=\dfrac{2}{35}\\ x=\dfrac{1}{5}:\dfrac{2}{35}=\dfrac{1}{5}.\dfrac{35}{2}=\dfrac{7}{2}\)

\(\dfrac{x}{5}+\dfrac{1}{2}=\dfrac{6}{10}\Leftrightarrow\dfrac{x}{5}=\dfrac{6}{10}-\dfrac{1}{2}\Rightarrow x=\dfrac{1}{10}\)

\(\dfrac{1}{2}.x+\dfrac{1}{2}=\dfrac{5}{2}\Leftrightarrow\dfrac{1}{2}.x=\dfrac{5}{2}-\dfrac{1}{2}\Leftrightarrow\dfrac{1}{2}.x=2\Leftrightarrow x=4\)

\(\dfrac{1}{2}-\dfrac{2}{3}.x=\dfrac{7}{12}\Leftrightarrow\dfrac{2}{3}.x=\dfrac{1}{2}+\dfrac{7}{12}\Leftrightarrow\dfrac{2}{3}.x=\dfrac{13}{12}\Leftrightarrow x=\dfrac{13}{12}:\dfrac{2}{3}\Leftrightarrow x=\dfrac{13}{8}\)

Bài 1:

a.

$|x+\frac{7}{4}|=\frac{1}{2}$

\(\Leftrightarrow \left[\begin{matrix} x+\frac{7}{4}=\frac{1}{2}\\ x+\frac{7}{4}=-\frac{1}{2}\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} x=\frac{-5}{4}\\ x=\frac{-9}{4}\end{matrix}\right.\)

b. $|2x+1|-\frac{2}{5}=\frac{1}{3}$
$|2x+1|=\frac{1}{3}+\frac{2}{5}$

$|2x+1|=\frac{11}{15}$

\(\Leftrightarrow \left[\begin{matrix} 2x+1=\frac{11}{15}\\ 2x+1=\frac{-11}{15}\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} x=\frac{-2}{15}\\ x=\frac{-13}{15}\end{matrix}\right.\)

c.

$3x(x+\frac{2}{3})=0$

\(\Leftrightarrow \left[\begin{matrix} 3x=0\\ x+\frac{2}{3}=0\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} x=0\\ x=\frac{-3}{2}\end{matrix}\right.\)

d.

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

$\Leftrightarrow x=\frac{2}{5}$

Bài 2:

$\frac{1}{100}-A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}$

$=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{100-99}{99.100}$

$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}=1-\frac{1}{100}$

$=\frac{99}{100}$

$\Rightarrow A=\frac{1}{100}-\frac{99}{100}=-\frac{98}{100}=\frac{-49}{50}$

Bài 1: 

a) Ta có: \(\left|x+\dfrac{7}{4}\right|=\dfrac{1}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{7}{4}=\dfrac{1}{2}\\x+\dfrac{7}{4}=\dfrac{-1}{2}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-5}{4}\\x=\dfrac{-9}{4}\end{matrix}\right.\)

b) Ta có: \(\left|2x+1\right|-\dfrac{2}{5}=\dfrac{1}{3}\)

\(\Leftrightarrow\left|2x+1\right|=\dfrac{11}{15}\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+1=\dfrac{11}{15}\\2x+1=\dfrac{-11}{15}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{-4}{15}\\2x=\dfrac{-26}{15}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-2}{15}\\x=\dfrac{-13}{15}\end{matrix}\right.\)

c) Ta có: \(3x\left(x+\dfrac{2}{3}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+\dfrac{2}{3}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{-2}{3}\end{matrix}\right.\)

a) Ta có: \(\dfrac{4}{5}-3\left|x\right|=\dfrac{1}{5}\)

\(\Leftrightarrow3\left|x\right|=\dfrac{4}{5}-\dfrac{1}{5}=\dfrac{3}{5}\)

\(\Leftrightarrow\left|x\right|=\dfrac{1}{5}\)

hay \(x\in\left\{\dfrac{1}{5};-\dfrac{1}{5}\right\}\)

b) Ta có: \(4x-\dfrac{1}{2}x+\dfrac{3}{5}x=\dfrac{4}{5}\)

nên \(\dfrac{41}{10}x=\dfrac{4}{5}\)

hay \(x=\dfrac{8}{41}\)

c) Ta có: \(\left(2x-8\right)\left(10-5x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-8=0\\10-5x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=8\\5x=10\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=2\end{matrix}\right.\)

d) Ta có: \(\dfrac{3}{4}+\dfrac{1}{4}\left|2x-1\right|=\dfrac{7}{2}\)

\(\Leftrightarrow\dfrac{1}{4}\left|2x-1\right|=\dfrac{7}{2}-\dfrac{3}{4}=\dfrac{14}{4}-\dfrac{3}{4}=\dfrac{11}{4}\)

\(\Leftrightarrow\left|2x-1\right|=11\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-1=11\\2x-1=-11\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=12\\2x=-10\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-5\end{matrix}\right.\)

a) x=4/2

b) x=1/12

c) 24/35

a,\(\dfrac{1}{2}+x=\dfrac{5}{2}\)

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

\(\Rightarrow x=2\)

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

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

\(\Rightarrow x=\dfrac{1}{12}\)

c,\(x:\dfrac{4}{5}=\dfrac{6}{7}\)

\(x=\dfrac{6}{7}.\dfrac{4}{5}\)

\(\Rightarrow\dfrac{24}{35}\)

a)1/2+x=5/2                                          b)3/4-x=2/3

    x=5/2-1/2=4/2=2                                  x=3/4-2/3=1/12

c)x:4/5=6/7

   x=6/7.4/5=24/35