Đáp án:
Bài 2)
$1) x=\dfrac{1}{4}\\
2) {\left[\begin{aligned} x=\dfrac{7}{10}\\ x=\dfrac{3}{10}\end{aligned}\right.}\\
3)
{\left[\begin{aligned} x=\dfrac{-4}{3}\\ x=2\end{aligned}\right.}\\
4)
x=\{-5,-4,-3,-2,-1,0\}$
Giải thích các bước giải:
Bài 2)
$1) x+\dfrac{7}{2}=\dfrac{15}{4}\\
\Leftrightarrow x=\dfrac{15}{4}-\dfrac{7}{2}\\
\Leftrightarrow x=\dfrac{15}{4}-\dfrac{14}{4}\\
\Leftrightarrow x=\dfrac{1}{4}\\
2) 0,8+\left | x-\dfrac{1}{2} \right |=1\\
\Leftrightarrow \left | x-\dfrac{1}{2} \right |=1-\dfrac{8}{10}\\
\Leftrightarrow \left | x-\dfrac{1}{2} \right |=1-\dfrac{4}{5}\\
\Leftrightarrow \left | x-\dfrac{1}{2} \right |=\dfrac{5}{5}-\dfrac{4}{5}\\
\Leftrightarrow \left | x-\dfrac{1}{2} \right |=\dfrac{1}{5}\\
\Leftrightarrow {\left[\begin{aligned}x-\dfrac{1}{2}=\dfrac{1}{5}\\x-\dfrac{1}{2}=-\dfrac{1}{5}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{1}{5}+\dfrac{1}{2}\\ x=-\dfrac{1}{5}+\dfrac{1}{2}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{2}{10}+\dfrac{5}{10}\\ x=-\dfrac{2}{10}+\dfrac{5}{10}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{7}{10}\\ x=\dfrac{3}{10}\end{aligned}\right.}\\
3)
\left ( \dfrac{1}{3}-x \right )^2-1\dfrac{3}{9}=1\dfrac{4}{9}\\
\Leftrightarrow \left ( \dfrac{1}{3}-x \right )^2-\dfrac{12}{9}=\dfrac{13}{9}\\
\Leftrightarrow \left ( \dfrac{1}{3}-x \right )^2=\dfrac{13}{9}+\dfrac{12}{9}\\
\Leftrightarrow \left ( \dfrac{1}{3}-x \right )^2=\dfrac{25}{9}=\left ( \dfrac{5}{3} \right )^2\\
\Leftrightarrow {\left[\begin{aligned}\dfrac{1}{3}-x=\dfrac{5}{3}\\ \dfrac{1}{3}-x=-\dfrac{5}{3}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{1}{3}-\dfrac{5}{3}\\ x=\dfrac{1}{3}+\dfrac{5}{3}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{-4}{3}\\ x=2\end{aligned}\right.}\\
4)
-1\leq \dfrac{x}{5}<\dfrac{1}{5}\\
\Leftrightarrow -5\leq x<1\\
\Rightarrow x=\{-5,-4,-3,-2,-1,0\}$
