/x+4/15/-/-3,75/=-/-2,15/

/x+4/15/-15/4=-\(\frac{43}{20}\)

x+4/15=\(\frac{43}{20}+\frac{15}{4}\)

x+4/15=59/10

    x=59/10-4/15

    x=\(5\frac{19}{30}\)

a) \(\left|x-1,7\right|+\dfrac{1}{2}=23\)

\(\left|x-1,7\right|=22,5\)

\(\Rightarrow x-1,7=\pm22,5\)

\(\Rightarrow x=\left\{24,2;-20,8\right\}\)

b) \(\left|x+\dfrac{4}{15}\right|-\left|3,75\right|=-\left|2,15\right|\)

\(\left|x+\dfrac{4}{15}\right|-3,75=-2,15\)

\(\left|x+\dfrac{4}{15}\right|=-2,15+3,75\)

\(\left|x+\dfrac{4}{15}\right|=1,6\)

\(\Rightarrow x+\dfrac{4}{15}=\pm1,6\)

\(\Rightarrow x=\left\{\dfrac{4}{3};-\dfrac{28}{15}\right\}\)

a)\(\left|x-1,7\right|+\dfrac{1}{2}=23\)

<=>\(\left|x-1,7\right|=22,5\)

<=>\(-\left(x-1,7\right)=-22,5\) hoặc \(x-1,7=22,5\)

<=>\(-x+1,7=-22,5\) hoặc \(x-1,7=22,5\)

<=>\(-x=-22,5-1,7\) hoặc \(x=22,5+1,7\)

<=>\(x=24,2\)

vậy \(x=24,2\)

a) \(\left|2,5-x\right|-1,3=0\)

th1: \(2,5-x\ge0\Leftrightarrow x\le2,5\)

\(\Rightarrow\left|2,5-x\right|-1,3=0\Leftrightarrow2,5-x-1,3=0\Leftrightarrow x=1,2\left(tmđk\right)\)

th2: \(2,5-x< 0\Leftrightarrow x>2,5\)

\(\Rightarrow\left|2,5-x\right|-1,3=0\Leftrightarrow x-2,5-1,3=0\Leftrightarrow x=3,8\left(tmđk\right)\)

vậy \(x=1,2;x=3,8\)

b) \(1,6.\left|x-0,2\right|=0\Leftrightarrow\left|x-0,2\right|=0\Leftrightarrow x-0,2=0\Leftrightarrow x=0,2\) vậy \(x=0,2\)

c) \(\left|\dfrac{1}{3}-x\right|-\left|\dfrac{-3}{7}\right|=0\)

th1: \(\dfrac{1}{3}-x\ge0\Leftrightarrow x\le\dfrac{1}{3}\)

\(\Rightarrow\left|\dfrac{1}{3}-x\right|-\left|\dfrac{-3}{7}\right|=0\Leftrightarrow\dfrac{1}{3}-x-\dfrac{3}{7}=0\Leftrightarrow x=\dfrac{-2}{21}\left(tmđk\right)\)

th2: \(\dfrac{1}{3}-x< 0\Leftrightarrow x>\dfrac{1}{3}\)

\(\Rightarrow\left|\dfrac{1}{3}-x\right|-\left|\dfrac{-3}{7}\right|=0\Leftrightarrow x-\dfrac{1}{3}-\dfrac{3}{7}=0\Leftrightarrow x=\dfrac{16}{21}\left(tmđk\right)\)

vậy \(x=\dfrac{-2}{21};x=\dfrac{16}{21}\)

d) \(\left|x+\dfrac{4}{15}\right|-\left|-3,75\right|=-\left|-2,15\right|\)

th1: \(x+\dfrac{4}{15}\ge0\Leftrightarrow x\ge\dfrac{-4}{15}\)

\(\Rightarrow\left|x+\dfrac{4}{15}\right|-\left|-3,75\right|=-\left|-2,15\right|\Leftrightarrow x+\dfrac{4}{15}-3,75=-2,15\)

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

th2: \(x+\dfrac{4}{15}< 0\Leftrightarrow x< \dfrac{-4}{15}\)

\(\Rightarrow\left|x+\dfrac{4}{15}\right|-\left|-3,75\right|=-\left|-2,15\right|\Leftrightarrow-x-\dfrac{4}{15}-3,75=-2,15\)

\(\Leftrightarrow x=\dfrac{-28}{15}\left(tmđk\right)\)

vậy \(x=\dfrac{4}{3};x=\dfrac{-28}{15}\)

e) ta có : \(\left|x-1,5\right|\ge0\forall x\) và \(\left|2,5-x\right|\ge0\forall x\)

\(\Rightarrow\left|x-1,5\right|+\left|2,5-x\right|=0\Leftrightarrow\left\{{}\begin{matrix}x-1,5=0\\2,5-x=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=1,5\\x=2,5\end{matrix}\right.\) 2 giá trị này khác nhau \(\Rightarrow\) phương trình vô nghiệm

a,x=7                b, x=.....

\(\frac{1}{2}x+\frac{1}{5}x+\frac{3}{5}=0\)

=> \(\left(\frac{1}{2}+\frac{1}{5}\right)x+\frac{3}{5}=0\)

=> \(\frac{7}{10}x+\frac{3}{5}=0\)

=> \(\frac{7}{10}x=-\frac{3}{5}\)

=> \(x=\left(-\frac{3}{5}\right):\frac{7}{10}=\left(-\frac{3}{5}\right)\cdot\frac{10}{7}=\left(-\frac{3}{1}\right)\cdot\frac{2}{7}=-\frac{6}{7}\)

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

=> \(\left|\frac{5}{2}+x\right|+\frac{2}{3}=3\)

=> \(\left|\frac{5}{2}+x\right|=\frac{7}{3}\)

=> \(\orbr{\begin{cases}\frac{5}{2}+x=\frac{7}{3}\\\frac{5}{2}+x=-\frac{7}{3}\end{cases}}\Rightarrow\orbr{\begin{cases}x=-\frac{1}{6}\\x=-\frac{29}{6}\end{cases}}\)

c) \(\left|x+\frac{4}{15}\right|-\left|-3.75\right|=-\left|-2,15\right|\)

=> \(\left|x+\frac{4}{15}\right|-3,75=-2,15\)

=> \(\left|x+\frac{4}{15}\right|=\frac{8}{5}\)

=> \(\orbr{\begin{cases}x+\frac{4}{15}=\frac{8}{5}\\x+\frac{4}{15}=-\frac{8}{5}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{4}{3}\\x=-\frac{28}{15}\end{cases}}\)

a, \(\frac{1}{2}x+\frac{1}{5}x+\frac{3}{5}=0\Leftrightarrow\frac{7}{10}x+\frac{3}{5}=0\Leftrightarrow x=-\frac{6}{7}\)

b, đề sai 

c, \(\left|\frac{x+4}{15}\right|-\left|-3,75\right|=-\left|-2,15\right|\)

\(\Leftrightarrow\frac{x+4}{15}-3,75=-2,15\Leftrightarrow\frac{x+4}{15}=\frac{8}{5}\Leftrightarrow x+4=24\Leftrightarrow x=28\)