Question

[Lê Minh Quang]

|3/2x-1|-|x+3/2|=0

 

Answer 1

[Nguyễn Việt Hoàng]

\(\left|\frac{3}{2}x-1\right|-\left|x+\frac{3}{2}\right|=0\)

Ta có :

\(\left|\frac{3}{2}x-1\right|-\left|x+\frac{3}{2}\right|\ge\left|\frac{3x}{2}-1-x-\frac{3}{2}\right|=\left|\frac{x-5}{2}\right|\)

Tự làm nốt

Answer 2

[Huyen Trang]

Ta có: \(\left|\frac{3}{2}x-1\right|-\left|x+\frac{3}{2}\right|=0\)

\(\Leftrightarrow\left|\frac{3}{2}x-1\right|=\left|x+\frac{3}{2}\right|\)

\(\Leftrightarrow\orbr{\begin{cases}\frac{3}{2}x-1=x+\frac{3}{2}\\\frac{3}{2}x-1=-x-\frac{3}{2}\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}\frac{1}{2}x=\frac{5}{2}\\\frac{5}{2}x=-\frac{1}{2}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=5\\x=-\frac{1}{5}\end{cases}}\)