Question

Tính tổng các số nguyên x biết:

1) \(\left|x\right|\le9\)

2) \(\left|x\right|-3\le7\)

3) \(\left|x-3\right|\le7\)

Answer 1

1) \(\left|x\right|\le9\)

\(\Rightarrow x\in\left\{-9;-8;-7;...;7;8;9\right\}\)

2) \(\left|x\right|-3\le7\)

\(\Rightarrow\left|x\right|\le7+3\)

\(\Rightarrow\left|x\right|\le10\)

\(\Rightarrow x\in\left\{-10;-9;-8;...;8;9;10\right\}\)

3) \(\left|x-3\right|\le7\)

\(\Rightarrow\left|x-3\right|\in\left\{0;1;2;3;4;5;6;7\right\}\)

\(\Rightarrow\left(x-3\right)\in\left\{-7;-6;-5;...;5;6;7\right\}\)

\(\Rightarrow x\in\left\{-4;-3;-2;...;8;9;10\right\}\)