Question

Tìm x thuộc Z, biết

|x+5|-7<20

|x+18|+13>21

Answer 1

\(a,\left|x+5\right|-7< 20\)

\(\Rightarrow\left|x+5\right|< 20+7\)

\(\Rightarrow\left|x+5\right|< 27\)

\(\Rightarrow\hept{\begin{cases}x+5< 27\\x+5>-27\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x< 27-5\\x>-27-5\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}x< 22\\x>-32\end{cases}}\)

\(\Rightarrow x\in\left\{-31;-30;...;20;21\right\}\)

\(b,\left|x+18\right|+13>21\)

\(\Rightarrow\left|x+18\right|>21-13\)

\(\Rightarrow\left|x+18\right|>8\)

\(\Rightarrow\orbr{\begin{cases}x+18>8\\x+18< -8\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x>-10\\x< -26\end{cases}}\)

\(\Rightarrow x\in\left\{...;-28;-27;-9;-8;...\right\}\)

~Study well~

#KSJ