Question

Mọi người giúp mình giải bài này với

Answer 1

\(\left|x-0,75\right|-3\dfrac{1}{2}=0\)

\(\Leftrightarrow\left|x-\dfrac{3}{4}\right|=3\dfrac{1}{2}\)

\(\Leftrightarrow\left|x-\dfrac{3}{4}\right|=\dfrac{7}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{3}{4}=\dfrac{7}{2}\\x-\dfrac{3}{4}=-\dfrac{7}{2}\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{17}{4}\\x=-\dfrac{11}{4}\end{matrix}\right.\)

Answer 2

\(PT\Rightarrow\left|x-\dfrac{3}{4}\right|=\dfrac{7}{2}\Rightarrow\left[{}\begin{matrix}x-\dfrac{3}{4}=\dfrac{7}{2}\\x-\dfrac{3}{4}=-\dfrac{7}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{17}{4}\\x=-\dfrac{11}{4}\end{matrix}\right.\)

Answer 3

Chuyển vế r tách trường hợp ra thôi bạn, 

\(\left|x-0,75\right|-3\dfrac{1}{2}=0\\ \Rightarrow\left|x-0,75\right|=3\dfrac{1}{2}=\dfrac{7}{2}\)

⇒\(\left|x-\dfrac{3}{4}\right|=\dfrac{7}{2}\)

⇒\(\left\{{}\begin{matrix}x-\dfrac{3}{4}=\dfrac{7}{2}\\x-\dfrac{3}{4}=-\dfrac{7}{2}\end{matrix}\right.\)

⇒\(\left\{{}\begin{matrix}x=\dfrac{7}{2}+\dfrac{3}{4}=\dfrac{17}{4}\\x=-\dfrac{7}{2}+\dfrac{3}{4}=-\dfrac{11}{4}\end{matrix}\right.\)

⇒ \(x\in\left\{\dfrac{17}{4};-\dfrac{11}{4}\right\}\)