\(\dfrac{2}{3}-\left|x-2,4\right|=\dfrac{1}{2}\)

\(\left|x-2,4\right|=\dfrac{2}{3}-\dfrac{1}{2}\)

\(\left|x-2,4\right|=\dfrac{1}{6}\)

*) Với \(x\ge2,4\) ta có:

\(x-2,4=\dfrac{1}{6}\)

\(x=\dfrac{1}{6}+2,4\)

\(x=\dfrac{77}{30}\) (nhận)

*) Với \(x< 2,4\) ta có:

\(x-2,4=-\dfrac{1}{6}\)

\(x=-\dfrac{1}{6}+2,4\)

\(x=\dfrac{67}{30}\) (nhận)

Vậy \(x=\dfrac{67}{30};x=\dfrac{77}{30}\)

a, \(\dfrac{3}{7}\)\(x\) - 0,4 = - \(\dfrac{17}{35}\)

    \(\dfrac{3}{7}\)\(x\)         = - \(\dfrac{17}{35}\) + 0,4

     \(\dfrac{3}{7}\)\(x\)       = - \(\dfrac{3}{35}\)

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

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

b, 0,2.(\(x\) - 3) +2,4 = 10

    0,2.(\(x\) - 3)          = 10 - 2,4

    0,2.(\(x\) - 3)          = 7,6

           \(x\) - 3            = 7,6:0,2

           \(x\) - 3            = 38

            \(x\)                = 38 + 3

             \(x\)                = 41

a: Sửa đề: \(A=\dfrac{\sqrt{x}+1}{\sqrt{x}-3}\)

ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x\ne9\end{matrix}\right.\)

Để A là số nguyên thì \(\sqrt{x}+1⋮\sqrt{x}-3\)

=>\(\sqrt{x}-3+4⋮\sqrt{x}-3\)

=>\(4⋮\sqrt{x}-3\)

=>\(\sqrt{x}-3\in\left\{1;-1;2;-2;4;-4\right\}\)

=>\(\sqrt{x}\in\left\{4;2;5;1;7;-1\right\}\)

=>\(\sqrt{x}\in\left\{4;2;5;1;7\right\}\)

=>\(x\in\left\{16;4;25;1;49\right\}\)

b: 

a) \(\left|x-1\right|=5\)

\(\Rightarrow\orbr{\begin{cases}x-1=5\\x-1=-5\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x=6\\x=-4\end{cases}}\)

b) \(\left|x-0,5\right|=2,4\)

\(\Rightarrow\orbr{\begin{cases}x-0,5=2,4\\x-0,5=-2,4\end{cases}}\Rightarrow\orbr{\begin{cases}x=2,9\\x=-1,9\end{cases}}\)

c) \(2\left|3x-1\right|-1=6\)

\(\Leftrightarrow2\left|3x-1\right|=7\)

\(\Leftrightarrow\left|3x-1\right|=3,5\)

\(\Rightarrow\orbr{\begin{cases}3x-1=3,5\\3x-1=-3,5\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}3x=4,5\\2x=-2,5\end{cases}\Rightarrow\orbr{\begin{cases}x=1,5\\-1,25\end{cases}}}\)

a)4 hoặc -4

b)1,9 hoặc -1,9

c)1,5

\(\dfrac{1}{2}x+2\dfrac{1}{2}=3\dfrac{1}{2}x.\left(-\dfrac{1}{3}\right)\\ \Rightarrow\dfrac{1}{2}x+\dfrac{5}{2}=\dfrac{7}{2}x.\left(-\dfrac{1}{3}\right)\\ \Rightarrow\dfrac{1}{2}x+\dfrac{5}{2}+\dfrac{7}{2}x=-\dfrac{1}{3}\\ \Rightarrow\left(\dfrac{1}{2}+\dfrac{7}{2}\right)x+\dfrac{5}{2}=-\dfrac{1}{3}\\ \Rightarrow4x=-\dfrac{17}{6}\\ \Rightarrow x=-\dfrac{17}{24}.\)

\(\dfrac{1}{2}x+2\dfrac{1}{2}=3\dfrac{1}{2}x-\dfrac{1}{3}\\ \Rightarrow\dfrac{1}{2}x-3\dfrac{1}{2}x=-\dfrac{1}{3}-2\dfrac{1}{2}\\ \Rightarrow\left(\dfrac{1}{2}-\dfrac{7}{2}\right)x=-\dfrac{1}{3}-\dfrac{5}{2}\\ \Rightarrow\dfrac{-6}{2}x=-\dfrac{17}{6}\\ \Rightarrow-3x=-\dfrac{17}{6}\\ \Rightarrow x=\left(-\dfrac{17}{6}\right):\left(-3\right)\\ \Rightarrow x=\dfrac{17}{18}\)

\(a,\dfrac{2}{3}x-\dfrac{2}{5}=\dfrac{1}{2}x-\dfrac{1}{3}\\ \Rightarrow\dfrac{2}{3}x-\dfrac{1}{2}x-\dfrac{2}{5}=-\dfrac{1}{3}\\ \Rightarrow x\left(\dfrac{2}{3}-\dfrac{1}{2}\right)-\dfrac{2}{5}=-\dfrac{1}{3}\\ \Rightarrow x\dfrac{1}{6}=-\dfrac{11}{15}\\ \Rightarrow x=-\dfrac{22}{5}\\ b,\dfrac{1}{3}x+\dfrac{2}{5}.\left(x+1\right)=0\\ \Rightarrow\dfrac{1}{3}x+\left(x+1\right)=-\dfrac{2}{5}\\ \Rightarrow\dfrac{1}{3}x=-\dfrac{2}{5}-\left(x+1\right)\\ \Rightarrow\dfrac{1}{3}x=-\dfrac{7}{5}-x\\ \Rightarrow\dfrac{1}{3}.2x=-\dfrac{7}{5}\\ \Rightarrow2x=-\dfrac{21}{5}\\ \Rightarrow x=-\dfrac{21}{10}.\)

1,\(\dfrac{-1}{4}-\dfrac{3}{4}:x=-\dfrac{11}{36}\)

\(-\dfrac{3}{4}:x=\left(-\dfrac{1}{4}\right)-\left(-\dfrac{11}{36}\right)\)

\(-\dfrac{3}{4}:x=\dfrac{1}{18}\)

\(x=\left(-\dfrac{3}{4}\right):\left(\dfrac{1}{18}\right)\)

\(x=\dfrac{27}{2}\)

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

\(\dfrac{3}{4}x=\dfrac{3}{7}+\dfrac{1}{2}\)

\(\dfrac{3}{4}x=\dfrac{13}{14}\)

\(x=\dfrac{13}{14}:\dfrac{3}{4}\)

\(x=\dfrac{26}{21}\)

1 , x = 36/11

2 , x = 26/21

a, - \(\dfrac{1}{10}\) + \(\dfrac{2}{5}\)\(x\) + \(\dfrac{7}{20}\) = \(\dfrac{1}{10}\)

              \(\dfrac{2}{5}\)\(x\)            = \(\dfrac{1}{10}\) - \(\dfrac{7}{20}\) + \(\dfrac{1}{10}\)

              \(\dfrac{2}{5}\) \(x\)           = - \(\dfrac{3}{20}\)

                  \(x\)          =  - \(\dfrac{3}{20}\): \(\dfrac{2}{5}\)

                  \(x\)          = - \(\dfrac{3}{8}\)

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

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

             \(\dfrac{1}{2}\): \(x\) = - \(\dfrac{8}{15}\)

                   \(x\) =  \(\dfrac{1}{2}\): (- \(\dfrac{8}{15}\))

                    \(x\) =  - \(\dfrac{15}{16}\)