Câu hỏi của Khánh Linh

Question

BT1: Tìm x, biết:

5) $\text{|}x+\dfrac{1}{3}\text{|}+\text{|}x+\dfrac{1}{5}\text{|}+\text{|}x+\dfrac{1}{15}\text{|}=4x$

Nguyễn Thanh Hằng · Accepted Answer

$\left|x+\dfrac{1}{3}\right|+\left|x+\dfrac{1}{5}\right|+\left|x+\dfrac{1}{15}\right|=4x$

Mà $\left\{{}\begin{matrix}\left|x+\dfrac{1}{3}\right|\ge0\\left|x+\dfrac{1}{5}\right|\ge0\\left|x+\dfrac{1}{15}\right|\ge0\end{matrix}\right.$

$\Leftrightarrow\left|x+\dfrac{1}{3}\right|+\left|x+\dfrac{1}{5}\right|+\left|x+\dfrac{1}{15}\right|\ge0$

$\Leftrightarrow4x\ge0$

$\Leftrightarrow x+\dfrac{1}{3}+x+\dfrac{1}{5}+x+\dfrac{1}{15}=4x$

$\Leftrightarrow3x+1=4x$

$\Leftrightarrow x=1$