问题 填空题
如果关于x的不等式(a-1)x<a+5和2x<4的解集相同,则a的值为______.
(1)一变:如果
(a-1)x<a+5
2x<4
的解集是x<2,则a的取值范围是______;
(2)二变:如果
2x<4
x≥1
x<
a+5
a-1
的解集是1≤x<2,则a的取值范围是______.
答案

2x<4的解集为x<2,

当a>1时,(a-1)x<a+5变形为x<

a+5
a-1

由不等式的解集相同,故

a+5
a-1
=2,

解得a=7;

(1)在(a-1)x<a+5中,

若a<1,则解得x>

a+5
a-1

不等式的解集就为2>x>

a+5
a-1
了,与原题矛盾,所以a>1.

∴(a-1)x<a+5的解集为x<

a+5
a-1

根据“同小取小”的原则可得

a+5
a-1
≥2,

解得:a≤7.

当a=1时,x<2符合题意,

∴a的取值范围是1≤a≤7;

(2)由2x<4得:x<2,

又∵该不等式的解集为1≤x<2.

根据“同小取小”的原则可得

a+5
a-1
≥2.

解得a≤7,

∴a的取值范围是1<a≤7.

阅读理解

阅读下列短文,从每个小题所给的选项中选出最佳答案。

     One afternoon Mrs Green's husband wanted to catch the 3:30 flight to London to have an

important meeting. She was very surprised when he telephoned her at 5 0'clock and said that

he was still at the airport.

     "What happened to you?" asked Mrs Green.  

     "Well," said Mr Green, "everything was going fine.  I got my ticket, checked my luggage 

and waited in line at the gate.  I walked across the  runway to the airplane and I saw my friend 

Jack Scott, who was an airplane engineer.  I shouted to him and a policeman caught me. "      

     "Why did he catch you?"         

     "I don't know," said Mr Green.  "As soon as he heard my shout, he ran towards me and 

caught me. "      

     "What did you shout to your friend?"       

      "All I said was 'Hi, Jack'.  You know that's the usual way we say hello to our friends. "      

      "But you don't know the sentence 'Hi, Jack' also means to take control of a plane by force (武力). " 

1. How did Mr Green want to go to London?   [ ]

A. By train.

B. By bus.

C. By airplane.

2. Why was Mrs Green surprised?  [ ]

A. Because her husband didn't arrive at the airport in time.

B. Because her husband was still at the airport at 5 0'clock.

C. Because her husband didn't want to go to London

3. When did Mr Green get to the airport that afternoon? [ ]

A. Before 3:30.

B. After 3:30.

C. At about 5:00.

4. What was Jack Scott in the passage? [ ]

A. He was a pilot.

B. He was a policeman at the airport.

C. He was an engineer.

5. According to the passage we know _____.[ ]

A. Jack Scott asked Mr Green not to fly to London

B. Mr Green would take control of a plane by force

C. the policemen mistook what Mr Green said

填空题