1. (Anhui senior high school entrance examination) Solving inequality: x3> 1-x-36.
Solution: Remove the denominator and get 2x & gt6-(x-3).
Without the brackets, you will get 2x>6 x+3.
Move items and merge similar items to get 3x >；; 9.
The coefficient is 1, x >；; 3.
2. (Daqing senior high school entrance examination) Solve the inequality about X: AX-X-2 >; 0.
Solution: through ax-x-2 >; 0，get(a- 1)x >； 2.
When a- 1=0, ax-x-2 >: 0 has no solution.
When a- 1 >; 0, then x & gt2a- 1.
When a- 1
3. Solve inequality 2 (x+ 1)
Solution: Remove the brackets and get 2x+2.
Move projects and merge similar projects into GET-X.
The coefficient is 1, x >；; 2.
Its solution set is expressed on the number axis as:
4. Solve inequality 2(x+ 1)- 1? 3x+2, and express its solution set on the number axis.
Solution: Remove the brackets and get 2x+2- 1? 3x+2。
Move items, get 2-3 times? 2-2+ 1.
Merge similar items and get -x? 1.
The coefficient is 1, x? - 1.
? The solution set of this inequality is x? -1, expressed on the number axis as follows:
5. Find the inequality 2x-7
Solution: Move the term to get 2x+2x.
Merge similar projects to get 4x.
The coefficient is 1, x.
? The positive integer solution of inequality is 1, 2.
6. known inequality x+8 >; The solution set of 4x+m(m is a constant) is X.
Solution: Move the item to get X-4x >; m-8。
Merge similar projects to get-3x > m-8。
The coefficient is 1, x.
The solution set of inequality is X.
? - 13(m-8)=3。
The solution is m=- 1.
The second kind of solutions of linear inequalities in one variable.
7. (Jinan senior high school entrance examination) Solving inequality group: 2x-1> 3、①2+2x？ 1+x.②
Solution: Solve inequality ① to get x>2.
Solve inequality ② and get x? - 1.
? The solution set of inequality group is x>2.
8. (Taizhou senior high school entrance examination) Solving inequality group: x-1> 2x，① 12x+3 & lt； - 1.②
Solution: Solve inequality ① and get X.
Solve inequality ② to get X.
? The solution set of inequality group is X.
9. Solve inequality group 2(x+2)? x+3，①x3
Solution: Solve inequality ① and get x? - 1.
Solve inequality ② to get X.
? Is the solution set of inequality group x? - 1.
The solution set of the inequality group is expressed on the number axis as:
10. Solve the inequality set 5x-2 >: 3(x+ 1), ① 12x-2? 7-52x, ② and represents the solution set of inequality group on the number axis.
Solution: Solve inequality ① to get x & gt52.
Solve inequality ② and get x? 3.
? The solution set of the inequality group is 52.
Its solution set is expressed on the number axis as:
1 1. Find the inequality set x-3? 2、① 1+ 12x & gt； Positive integer solution of 2x②.
Solution: Solve inequality ① and get x? 5.
Solve inequality ② to get X.
? The solution set of inequality group is X.
? This inequality group has no positive integer solution.
12. (Shiyan Senior High School Entrance Examination) When X takes integer value, inequality 5x+2 & gt；; 3(x- 1) and 12x? 2-32x are valid?
Solution: Solve the inequality group 5x+2 >； according to the meaning of the question; 3(x- 1)，① 12x？ 2-32x。 ②
Solve inequality ① and get x & gt-52.
Solve inequality ② and get x? 1.
? -52
So the integers that meet the conditions are -2,-1, 0, 1.
13. (Hohhot senior high school entrance examination) If the solution of binary linear equations 2x+y=-3m+2 and x+2y=4 satisfies x+y >; -32, find all positive integer values of m that meet the conditions.
Solution: 2x+y=-3m+2, ① x+2y = 4.
①+②，3(x+y)=-3m+6，
? x+y=-m+2。
∵x+y & gt； -32,
? -m+2 & gt； -32.
? m & lt72.
∵m is a positive integer,
? M= 1, 2 or 3.
14. Known: 2a-3x+ 1=0, 3b-2x- 16=0, while a? four
Solution: from 2a-3x+ 1=0, 3b-2x- 16=0, we can get
a=3x- 12，b=2x+ 163。
∵a？ four
? 3x- 12？ 4、①2x+ 163 & gt； 4.②
Solve inequality ① and get x? 3.
Solve inequality ② to get x & gt-2.
? The value range of x is -2.