－＜2a+3b＜

∵a+b，a－b的范围已知，

∴要求2a+3b的取值范围，

只需将2a+3b用已知量a+b，a－b表示出来.

可设2a+3b=x（a+b）+y（a－b），用待定系数法求出x、y.

设2a+3b=x（a+b）+y（a－b），

∴解得

∴－＜（a+b）＜，

－2＜－（a－b）＜－1.

∴－＜（a+b）－（a－b）＜，

即－＜2a+3b＜.

错解：解此题常见错误是：－1＜a+b＜3，                                                            ①

2＜a－b＜4.                                                                                                           ②

①+②得1＜2a＜7.                                                                                                 ③

由②得－4＜b－a＜－2.                                                                                         ④

①+④得－5＜2b＜1，∴－＜3b＜.                                                                ⑤

③+⑤得－＜2a+3b＜.