Câu hỏi của Quỳnh Ngân

Question

Bài 1: Tìm x :

a ) $\left|x+\frac{1}{2}\right|=\left|2x+3\right|$

b) \(\left|x+\frac{1}{5}\right|+\left|x+\frac{2}{5}\right|+\left|x+1...

soyeon_Tiểubàng giải · Accepted Answer

a) $\left|x+\frac{1}{2}\right|=\left|2x+3\right|$

$\Rightarrow\left[\begin{array}{nghiempt}x+\frac{1}{2}=2x+3\x+\frac{1}{2}=-\left(2x+3\right)\end{array}\right.$$\Rightarrow\left[\begin{array}{nghiempt}2x-x=\frac{1}{2}-3\x+\frac{1}{2}=-2x-3\end{array}\right.$

$\Rightarrow\left[\begin{array}{nghiempt}x=\frac{-5}{2}\x+2x=-3-\frac{1}{2}\end{array}\right.$$\Rightarrow\left[\begin{array}{nghiempt}x=\frac{-5}{2}\3x=\frac{-7}{2}\end{array}\right.$$\Rightarrow\left[\begin{array}{nghiempt}x=\frac{-5}{2}\x=\frac{-7}{6}\end{array}\right.$

Vậy $x\in\left\{\frac{-5}{2};\frac{-7}{6}\right\}$

Câu trả lời:

a) $\left|x+\frac{1}{2}\right|=\left|2x+3\right|$

$\Rightarrow\left[\begin{array}{nghiempt}x+\frac{1}{2}=2x+3\x+\frac{1}{2}=-\left(2x+3\right)\end{array}\right.$$\Rightarrow\left[\begin{array}{nghiempt}2x-x=\frac{1}{2}-3\x+\frac{1}{2}=-2x-3\end{array}\right.$

$\Rightarrow\left[\begin{array}{nghiempt}x=\frac{-5}{2}\x+2x=-3-\frac{1}{2}\end{array}\right.$$\Rightarrow\left[\begin{array}{nghiempt}x=\frac{-5}{2}\3x=\frac{-7}{2}\end{array}\right.$$\Rightarrow\left[\begin{array}{nghiempt}x=\frac{-5}{2}\x=\frac{-7}{6}\end{array}\right.$

Vậy $x\in\left\{\frac{-5}{2};\frac{-7}{6}\right\}$

Lê Yên Hạnh · Answer

$\left|x+\frac{1}{2}\right|=\left|2x+3\right|$

$Ta$ $có$: $x+\frac{1}{2}=2x+3$

$x+\frac{1}{2}=x+x+3\$

$x+\frac{1}{2}=x+\left(x+3\right)$

$\Rightarrow\frac{1}{2}=x+3$

$\Rightarrow x=\frac{1}{2}-3$

$\Rightarrow x=-\frac{5}{2}$

Vậy $x=-\frac{5}{2}$

b, $\left|x+\frac{1}{5}\right|+\left|x+\frac{2}{5}\right|+\left|x+1\frac{2}{5}\right|=4x$

$Ta$ $có$

$x+\frac{1}{5}+x+\frac{2}{5}+x+1\frac{2}{5}$$=4x$

$3x+\left(\frac{1}{5}+\frac{2}{5}+1\frac{2}{5}\right)=4x$

$3x+2=4x$

$3x+2=3x+x$

$\Rightarrow x=2$

Vậy $x=2$