1. Write an inequality X-2 > 3 _ _. The inequality X-2 > 3 has _ _ solutions.

Answer 6, there are countless.

2. The solution set of inequality -3x ≥ 12 is _ _ _, and the solution set of inequality 5x- 1 < 3 is _ _ _ _ _.

Note that when both sides of -3x ≥ 12 are divided by -3, the unequal symbols should be reversed.

The answer x ≤-4, x

3. the positive integer solution of inequality x+ 1 ≤ 3 is _ _ _, and the negative integer solution of inequality x+3 >- 1 is _ _.

Answer 1, 2; -3,-2,- 1.

4. The nonnegative integer solution of inequality 2x- 1 ≤ 9 is _ _, and the smallest integer solution of inequality 3x- 1 > 8 is _ _.

It is suggested that non-negative integer solutions should be 0 and positive integer solutions; The smallest integer solution refers to the smallest integer in the solution set.

Answer 0, 1, 2, 3, 4, 5; 4.

5. if the solution set of inequality 3x > A is x >-5, then the value of a is _ _ _ _. The answer is A =- 15.

It is suggested that from the meaning of the question, it is =-5, and the value of a can be obtained.

6. if the solution set of (a- 1) x > 2 is x.

Answer A < 1. It is suggested that if both sides of the inequality are divided by A- 1, the inequality sign will change direction, indicating that A- 1 is negative, that is, A- 1 < 0.

(2) multiple choice questions:

7. the solution set of inequality -2 (1-x) >-4 can be expressed as ... () on the number axis.

(A) (B)

(C) (D)

It is suggested that two sides of the inequality be divided by -2 to get 1-x < 2, and two sides plus x minus 2 to get X >- 1. Therefore, (c) is correct.

Answer C.

8. The number of nonnegative integer solutions satisfying the inequality -3 ≤ x ≤ 2 is ................. ().

1 (B)2 (C)3 (D)4

Prompt is a positive integer between 2 and -3 and 0, including 2. Answer C.

9. The following statement is correct in ............................... ().

(a) 2x- 1 > 0 when 2 x≥0 has the same solution set.

(b) The solution sets of b)x > 3 and x > 2 are the same.

(c) (x- 1) > 1 has the same solution set as x- 1 > 1.

(d) The solution set of 3 (2-x) >1is the same as that of 3 (x-2).

It is proposed that the solution set of inequality 2x- 1 is x >, while the solution set of inequality 2x- 1 ≥ 0 is x≥, and the difference between the two sets is one element x =, so (a) can be excluded. Represent the solution sets of x > 3 and x > 2 on the number axis. (b) can be excluded; The deformation of simplified inequality can exclude (c). Answer D.

10. ............ () is wrong in the following statement.

(a)- is the solution of the inequality x+ 1 < 2; (b) Solution Set of Inequality 5x+2

(c)X- 1 < 4 has infinite positive integer solutions; (d) A finite nonnegative integer solution with only 2x- 1 ≤ 3.

It is proposed that the solution of x- 1 < 4 leads to x < 5, and its positive integer solution is 1, 2, 3, 4 instead of infinite number. Therefore, choose (c). Answer C.

1 1. The solution set of inequality (a-3) x < a-3 is x > 1, and the following conclusion holds ().

(a) A ≠ 3 (b) A > 3 (c) A < 3 (d) A are all rational numbers.

It is suggested to divide both sides of (a-3) x < a-3 by a-3 to get the solution set x > 1. From the nature of inequality, we know that a-3 < 0, so a < 3. Therefore, we choose (c).

12. Represents the following set of inequality solutions on the number axis:

( 1)| x |-2>0 (2)| x |0

The mistake is ........................................................................... ().

(A)( 1) and (4)(B)(2) and (3)(C)(2) and (4)(D)( 1) and (3).

The hint can be judged by the meaning of the absolute value. The solution set of (2) does not contain 2, so a hollow point should be used. So (2) is wrong, and (a) and (d) are excluded; And the solution set of (4) | x | > 0 is x≠0, that is, (4) is wrong, so (c) is chosen.

(3) Answer questions:

13. Express the solution set of the following inequality on the number axis:

( 1)x > 1； (2)x 0，x ≤-。

2. The solution of the inequality group is _ _ _ _ _ _ _ _, and its negative integer solution is _ _ _ _ _ _ _.

Prompt "take medium". The answer is -3 ≤ x < 2, -3, -2,-1.

3. The minimum integer solution of the inequality group is _ _ _ _ _ _ _ _.

Suggested solution set x ≥ 3. Answer 4.

4. If the value of algebraic expression is greater than-1 less than 4, the value range of x is _ _ _ _ _ _ _ _.

According to the meaning of the question, you get-1 < < 4, and the answer is-1< x.

5. If a < b is known, the solution set of the inequality group is _ _ _ _ _ _ _.

Prompt "less than big and greater than small, should take the middle". Answer a ≤ x < B.

(2) True or false:

6. The solution set of inequality group is x >- 1 or x < 2 ....................................................... ().

It is suggested that x >- 1 or x < 2 does not all satisfy-1 < x < 2. Answer X.

7. Inequality group has no solution ............................... ()

It is suggested that x > 1 and x≤ 1 have no common parts. Answer √.

8.x =-2 is the integer solution of inequality group .............................................................. ().

It is proposed that x =-2 is in the solution set of inequality group -3 < x < 1 The answer is √.

(3) multiple choice questions:

9. Among the following inequality groups, the one whose solution set is -3 ≤ x < 5 is ……………………………………… ().

(A) (B) (C) (D)

It is suggested that (a) and (b) should be excluded according to the principle of "taking the largest with the largest" and "taking the smallest with the smallest"; (d) It is a set of contradictory inequalities, which can also be excluded.

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(A) (B)

(C) (D) answer D.

The solution set of 1 1. inequality group is ....................... ().

(a) When x ≤ 2 (b A)x≤2 (B)-3 a, the solution set should be x < a. Answer B.

13. if the solution set of inequality group (a≠b) is A < X < B, then the relationship between a and b is … ().

(A)a>b (B)ab>0 (D)a