Bài 4:

$x-2=|x+1|+|2x-3|\geq 0$

$\Rightarrow x\geq 2$

$\Rightarrow x+1>0; 2x-3>0$

$\Rightarrow |x+1|=x+1; |2x-3|=2x-3$. Khi đó:

$x+1+2x-3=x-2$

$\Leftrightarrow 3x-2=x-2\Leftrightarrow x=0$ (vô lý vì $0< 2$)

Vậy không tồn tại $x$ thỏa mãn.

Bài 5:

Nếu $x\geq 3$ thì $|x-1|=x-1; |x-2|=x-2; |x-3|=x-3$. Khi đó:

$x-1+x-2+x-3=5$

$\Leftrightarrow 3x-6=5\Leftrightarrow x=\frac{11}{3}$ (tm)

Nếu $2\leq x< 3$ thì $|x-1|=x-1; |x-2|=x-2; |x-3|=3-x$. Khi đó:

$x-1+x-2+3-x=5$

$\Leftrightarrow 2x=5\Leftrightarrow x=\frac{5}{2}$ (tm)

Nếu $1\leq x< 2$ thì: $x-1+2-x+3-x=5$

$\Leftrightarrow 4-x=5\Leftrightarrow x=-1$ (không tm)

Nếu $x< 1$ thì: $1-x+2-x+3-x=5$

$\Leftrightarrow 6-3x=5\Leftrightarrow x=\frac{1}{3}$ (tm)

Vậy......

Bài 4:

\(\left|x+1\right|+\left|2x-3\right|=x-2\)

\(\Leftrightarrow x-2=\left|x+1\right|+\left|2x-3\right|\ge0\)

\(\Leftrightarrow x\ge2\)

\(\Leftrightarrow x+1>0\Leftrightarrow\left|x+1\right|=x+1\)

\(\Leftrightarrow2x-3>0\Leftrightarrow\left|2x-3\right|=2x-3\)

Lúc đó:

\(x+1+2x-3=x-2\)

\(\Leftrightarrow3x-2=x-2\Leftrightarrow x=0\)(Vô lý)

Bài 5:

\(\left|x-1\right|+\left|x-2\right|+\left|x-3\right|=5\)

Trường hợp 1: \(x\ge3\)

\(\left|x-1\right|=x-1\)

\(\left|x-2\right|=x-2\)

\(\left|x-3\right|=x-3\)

Lúc đó:

\(x-1+x-2+x-3=5\)

\(\Leftrightarrow3x-6=5\Leftrightarrow x=\frac{11}{3}\)(Thỏa mãn)

Trường hợp 2: \(2\le x\le3\)

\(\left|x-1\right|=x-1\)

\(\left|x-2\right|=x-2\)

\(\left|x-3\right|=3-x\)

Lúc đó:

\(x-1+x-2+3-x=5\)

\(\Leftrightarrow2x=5\Leftrightarrow x=\frac{5}{2}\)(Thỏa mãn)

Trường hợp 3:\(1\le x\le2\)

\(\left|x-1\right|x=x-1\)

\(\left|x-2\right|=2-x\)

\(\left|x-3\right|=3-x\)

Lúc đó:

\(x-1+2-x+3-x=5\)

\(\Leftrightarrow4-x=5\Leftrightarrow x=\left(-1\right)\)(Loại)

Trường hợp 4: \(x< 1\)

\(\left|x-1\right|=1-x\)

\(\left|x-2\right|=2-x\)

\(\left|x-3\right|=3-x\)

Lúc đó:

\(1-x+2-x+3-x=5\)

\(\Leftrightarrow6-3x=5\Leftrightarrow x=\frac{1}{3}\)(Thỏa mãn)

3|x-1| + 2|x-1|=3|x-1|+4

2|x-1|=(3|x-1|+4)-3|x-1|

2|x-1|=4

|x-1|=4ơ:2

|x-1|=2

=>x-1=2 =>x=2-1=1

=>x-1= -2 =>x= -2 -1=-3

vậy x ∈ { -3 ; 1 }

Cảm ơn bạn nhé, nhưng mik thấy chỗ

=>x-1=2=>x=2+1=>x=3

=>x-1=-2=>x=-2+1=>x=-1

chứ ko như bạn ghi đúng ko?

Số 2

\(\left|x-1\right|+\left|1-x\right|=4-x\)

\(\Leftrightarrow\left|x-1\right|+\left|x-1\right|=4-x\)

\(\Leftrightarrow2\left|x-1\right|=4-x\)

\(\Leftrightarrow\left|x-1\right|=\frac{4-x}{2}\)

Xét \(x\ge1\):

\(pt\Leftrightarrow x-1=\frac{4-x}{2}\)

\(\Leftrightarrow\frac{2\left(x-1\right)}{2}-\frac{4-x}{2}=0\)

\(\Leftrightarrow\frac{2x-2-4+x}{2}=0\)

\(\Leftrightarrow3x-6=0\)

\(\Leftrightarrow x=2\)( thỏa mãn )

Xét \(x< 1\):

\(pt\Leftrightarrow1-x=\frac{4-x}{2}\)

\(\Leftrightarrow\frac{2\left(1-x\right)}{2}-\frac{4-x}{2}=0\)

\(\Leftrightarrow\frac{2-2x-4+x}{2}=0\)

\(\Leftrightarrow-x-2=0\)

\(\Leftrightarrow x=-2\)( thỏa mãn )

Vậy....

MƠN BẠN TRẦN PHƯƠNG THANH NHA