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Special topic on solving one-dimensional linear inequality in seventh grade mathematics
As the saying goes:? There is no sweetness without suffering. ? This is the pain and joy in learning. If you want to master real knowledge and skills, you can't do it without suffering. This year, the Graduate Examination Network searched and sorted out the problem of solving a linear inequality (group) in seventh grade mathematics 20 17, hoping to help everyone learn.

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.