kho

kho

a, \(\left|2x+1\right|=5\Rightarrow2x+1\in\left\{5;-5\right\}\)

+) Nếu :\(2x+1=5\Rightarrow2x=4\Rightarrow x=4\div2=2\)

+) Nếu : \(2x+1=-5\Rightarrow2x=-6\Rightarrow x=-6\div2=-3\)

Vậy \(x\in\left\{2;-3\right\}\)

b, \(\left|x-4\right|=\left|2-x\right|\)

\(\Rightarrow\left[\begin{matrix}x-4=2-x\\x-4=-\left(2-x\right)\end{matrix}\right.\)

+) Nếu : x - 4 = 2 - x

\(\Rightarrow x+x=2+4\Rightarrow2x=6\Rightarrow x=3\)

+) Nếu : x - 4 = - ( 2 - x )

\(\Rightarrow x-4=-2+x\Rightarrow x-x=-2+4\Rightarrow0=2\) ( loại )

Vậy x = 3 thỏa mãn đề bài

c, \(\left|x-5\right|=2-x\Rightarrow\left|x-5\right|+x=2\)

+) Nếu : \(x< 5\Rightarrow x-5< 5-5\Rightarrow x-5< 0\Rightarrow\left|x-5\right|=-x+5\)

Thay vào đề , ta có :

\(-x+5+x=2\Rightarrow-x+x+5=2\Rightarrow5=2\) ( loại )

+) Nếu : \(x\ge5\Rightarrow x-5\ge5-5\Rightarrow x-5\ge0\Rightarrow\left|x-5\right|=x-5\)

Thay vào đề , ta có :

\(\left(x-5\right)-x=2\Rightarrow x-5-x=2\)

\(\Rightarrow x-x-5=2\Rightarrow-5=2\) ( loại )

Vậy \(x\in\varnothing\)

\(\left|x-5\right|=5-x\)

\(\Rightarrow\left[\begin{array}{nghiempt}5-x=x-5\\5-x=-\left(x-5\right)\end{array}\right.\)

\(\Rightarrow\left[\begin{array}{nghiempt}5+5=x+x\\5-x=-x+5\end{array}\right.\)

\(\Rightarrow\left[\begin{array}{nghiempt}10=2x\\x\le5\end{array}\right.\Rightarrow\left[\begin{array}{nghiempt}x=5\\x\le5\end{array}\right.\)

Vậy \(x=5\) hoặc \(x\le5\) thõa mãn đề bài .

\(\left|x-5\right|=5-x\)

\(\Rightarrow\left[\begin{array}{nghiempt}x-5=5-x\\5-x=5-x\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x=5\\x\in R\end{array}\right.\)

Vậy x là số thực

\(\left|x-5\right|=5-x\)

\(\Rightarrow\left\{\frac{5-x=x-5}{5-x=-\left(x-5\right)}\right\}\)

\(\Rightarrow\left\{\frac{5+5=x+x}{5-x=-x+5}\right\}\)

\(\Rightarrow\begin{cases}10=2x\\x\le5\end{cases}\Rightarrow\begin{cases}x=5\\x\le5\end{cases}}\)

Ta có: \(\frac{x-3}{x+5}=\frac{5}{7}\)

\(\Rightarrow7.\left(x-3\right)=5.\left(x+5\right)\)

\(\Rightarrow7x-21=5x+25\)

\(\Rightarrow7x-5x=21+25=46\)

\(\Rightarrow2x=46\)

\(\Rightarrow x=46:2=23\)

Vậy x = 23

Ủng hộ mik nha!