Question

1．已知不等式$\left\{\begin{array}{l}{x＞a}\\{x＜b}\end{array}\right.$无解，求不等式组$\left\{\begin{array}{l}{x＞1-a}\\{x＜1-b}\end{array}\right.$的解．

Answer 1

分析 由不等式$\left\{\begin{array}{l}{x＞a}\\{x＜b}\end{array}\right.$无解，则a≥b，再解不等式即可．

解答 解：∵不等式$\left\{\begin{array}{l}{x＞a}\\{x＜b}\end{array}\right.$无解，
∴a≥b，
∴当a＞b时，等式组$\left\{\begin{array}{l}{x＞1-a}\\{x＜1-b}\end{array}\right.$的解集为1-a＜x＜1-b
当a=b时，等式组$\left\{\begin{array}{l}{x＞1-a}\\{x＜1-b}\end{array}\right.$无解．

点评 本题考查了含有字母参数的不等式组的解法，解此题的关键是先确定两个字母参数的大小关系．