làm tiếp cái trước(ấn nhầm)

\(x=\frac{5}{42}-\frac{15}{28}\) 

\(x=\frac{5.4}{6.4.7}-\frac{15.6}{4.7.6}\)

\(x=\frac{20}{168}-\frac{90}{168}\)

\(x=\frac{-70}{168}\)

\(x=\frac{-5}{12}\)

2. 

1.

 \(\frac{11}{13}-\left(\frac{5}{42}-x\right)=-\left(\frac{15}{28}-\frac{11}{13}\right)\)

\(\frac{11}{13}-\frac{5}{42}+x=-\frac{15}{28}+\frac{11}{13}\)

\(\frac{11}{13}-\frac{11}{13}-\frac{5}{42}+\frac{15}{28}=-x\)

/x+\(\frac{4}{15}\)/ \(-\)\(3,75\)\(=\)\(-2,15\)

/ \(x+\frac{4}{15}\)/ \(=\)\(-2,15+3,75\)

/ \(x+\frac{4}{15}\)/ \(=\)\(\frac{8}{5}\)

TH1: \(x+\frac{4}{15}=\frac{8}{5}\)                                          TH2: \(x+\frac{4}{15}=-\frac{8}{5}\)

\(=>x=\frac{8}{5}-\frac{4}{15}\)                                    \(=>x=-\frac{8}{5}-\frac{4}{15}\)

\(=>x=\frac{24}{15}-\frac{4}{15}\)                                   \(=>x=-\frac{24}{15}-\frac{4}{15}\)

\(=>x=\frac{20}{15}\)                                                 \(=>x=-\frac{28}{15}\)

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

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

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

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

\(\Rightarrow\orbr{\begin{cases}x+\frac{4}{15}=1,6\\x+\frac{4}{15}=-1,6\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{4}{3}\\x=\frac{-28}{15}\end{cases}}}\)

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

|x+4/15|=1,6

+)x+4/15=1,6

x=4/3

+)x+4/15=-1,6

x=-28/15

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

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

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

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

Ta có 2 trường hợp

trường hợp 1

\(x+\frac{4}{15}=1,6\)

\(x=1,6-\frac{4}{15}\)

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

Trường hợp 2

\(x+\frac{4}{15}=-1,6\)

\(x=-1,6-\frac{4}{15}\)

\(x=\frac{-28}{15}\)

Vậy \(x=\left\{-\frac{28}{15};\frac{4}{3}\right\}\)

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

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

\(\Leftrightarrow\left|x+\dfrac{4}{15}\right|=\dfrac{8}{5}\)

\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{4}{15}=\dfrac{8}{5}\\x+\dfrac{4}{15}=-\dfrac{8}{5}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=-\dfrac{28}{15}\end{matrix}\right.\)

\(\Rightarrow\left|x+\dfrac{4}{15}\right|-3,75=-2,15\\ \Rightarrow\left|x+\dfrac{4}{15}\right|=1,6=\dfrac{8}{5}\\ \Rightarrow\left[{}\begin{matrix}x+\dfrac{4}{15}=\dfrac{8}{5}\\x+\dfrac{4}{15}=-\dfrac{8}{5}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=-\dfrac{28}{15}\end{matrix}\right.\)

\(|x+3|+|2-x|\ge|x+3+2-x|=5\Rightarrow B_{min}=5\)

\(B=\left|x+3\right|+\left|2-x\right|\ge\left|x+3+2-x\right|=\left|5\right|=5\)

Dấu "=" xảy ra khi \(x=0\)

Vậy \(B_{min}=5\Leftrightarrow x=0\)

Áp dụng BĐT \(\left|x\right|+\left|y\right|\ge\left|x+y\right|\),ta được:

\(\left|x+3\right|+\left|2-x\right|\ge\left|\left(x+3\right)+\left(2-x\right)\right|=\left|5\right|=5\)

Vậy \(B_{min}=5\)\(\Leftrightarrow\left|x+3\right|+\left|2-x\right|=5\)

Xét \(x+3=0\Leftrightarrow x=-3;x+3>0\Leftrightarrow x>-3;x+3< 0\Leftrightarrow x< -3\)

      \(2-x=0\Leftrightarrow x=2;2-x>0\Leftrightarrow x< 2;2-x< 0\Leftrightarrow x>2\)

Ta có bảng xét dấu các đa thức x + 3 và 2 - x dưới đây:

*Xét khoảng x < -3 thì \(\left(-x-3\right)+\left(x-2\right)=5\Leftrightarrow-5=5\)(vô lí)

*Xét khoảng \(-3\le x\le2\)thì \(\left(x+3\right)+\left(x-2\right)=5\Leftrightarrow2x=4\Leftrightarrow x=2\)(giá trị này thuộc khoảng đang xét)

*Xét khoảng x > 2 thì \(\left(x+3\right)+\left(2-x\right)=5\Leftrightarrow5=5\)(t/m với mọi \(-3\le x\le2\))

Vậy \(B_{min}=5\)(Dấu '='\(\Leftrightarrow-3\le x\le2\))

│x+14/15│-3,75=-2,15

│x+14/15│=-2,15+3,75=1,6

Suy ra :

TH1 :x+14/15=1,6

x=2/3

TH2 :x+14/15=-1,6

x=-38/15

\(\left|x+\dfrac{14}{15}\right|-\left|-3,75\right|=-\left|-2,15\right|\)

\(\Leftrightarrow\left|x+\dfrac{14}{15}\right|-3,75=-2,15\)

\(\Leftrightarrow\left|x+\dfrac{14}{15}\right|=-2,15+3,75\)

\(\Leftrightarrow\left|x+\dfrac{14}{15}\right|=1,6\)

\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{14}{15}=-1,6\\x+\dfrac{14}{15}=1,6\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-38}{15}\\x=\dfrac{2}{3}\end{matrix}\right.\)

Vậy....

Chúc các bạn học tốt !!!

│x+14/15│-3,75=-2,15

│x+14/15│=-2,15+3,75=1,6

Suy ra :

TH1 :x+14/15=1,6

x=2/3

TH2 :x+14/15=-1,6

x=-38/15