Example 1. Multiple choice problem

(1) If the solution set of inequality (a+ 1) x > (a+ 1) x < 1, then [] must be satisfied.

(A)a- 1 (D)a B (or AX < B), and then compare it with the known solution (such as X < in (1)). Therefore, according to the nature of inequality, we can determine whether the coefficient A of X should be positive or negative. It is also necessary to calculate the numerical value to determine what the two sides of the inequality are divided by, and then determine the conditions that A should meet. (3) You can use the special value method to choose the answer, because only one conclusion is correct, so as long as it is 0.

Solution: (1) ∵ x < 1 is the solution of inequality (a+ 1) x > a+ 1, and there is a+ 1 < 0 according to inequality property 3.

∴ a

(2)∫(3a-2)x+2 < 3

Example 2. Analysis: first draw the number axis; Secondly, find out the position of the corresponding number on the number axis:-3,0,2,-1/2 of the four small questions in this example; Third, decide whether to draw solid points or hollow points, such as (2)(3) solid points and (1)(4) hollow points.

Solution: As shown in the figure.

Example 3

Solution: (a) (c); (b)(b)； (c)(d)； (d) (a)

Note: (a) means all rational numbers greater than or equal to 2, that is, all rational numbers not less than 2. Option (c);

In (b), all rational numbers between -2 and +2 are represented, that is, all rational numbers greater than -2 and less than 2. Option (b);

For all rational numbers less than -2 expressed in (c), select (d);

In (d), select all rational numbers located on the left side of -2 and the right side of +2 on the number axis, that is, rational numbers (a) less than -2 or greater than 2.

Exploration and application of verb (abbreviation of verb): (***20 points)

27.(8 points) Known:; ;

; According to this rule, then:

( 1) ;

(2) If yes, can you find the value of the algebraic expression according to the above laws?

1. Proof: (1) In Rt△ABC and Rt△ABD,

AC=AD，AB=AB，

∴Rt△ABC≌Rt△ABH(HL)

∴∴∠ 1=∠2 a is on the bisector of ∠CBD.

②∫Rt△ABC≌Rt△ABD，

∴BC=BD.

On the △BEC and △ beds,

BC=BD，∠ 1=∠2，BE=BE，

∴△BEC≌△BED(SAS)，

∴CE=DE.

Competition question: (I'm reading, too. I don't have an answer. Please forgive me! )

19, (10) When an isosceles triangle is divided into two smaller triangles by a straight line, what is the vertex angle of the original isosceles triangle? How to draw this straight line? Discuss all possible solutions and draw pictures one by one. )

20.( 12 minutes) Two cars start from the same place at the same time and drive straight in the same direction at the same speed. Each car can only take 24 barrels of gasoline at most, and no other oil can be used on the way. A barrel of oil can move a car 60 kilometers forward. Both cars must return to the starting point, but they can return at different times or borrow each other's gasoline. In order to keep one car as far away from the starting point as possible, the other car should also be far away from the starting point. How many kilometers has the car far from the starting point traveled?

14, there are 8 people in the classroom. Everyone shakes hands with others once and only once, and then * * * shakes hands twice;

During the spring outing, a class of 48 people will go boating in Jiang Xinyu. 3 persons per boat, rent 16 yuan. Each big ship takes 5 people and rents 24 yuan. Then this class will have to spend at least _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.