มาฝึกทำโจทย์ Math G.9 เรื่อง Linear Inequalities in One Variable. + Answer&Key

Verify whether the number given in brackets [ ] in each of the following problems is a solution to the corresponding inequality.

1.  x + 3 > 9 [6] 
2.  2x - 1 < 3 [-3]
3.  7x + 4 > 18 [5] 
4.  2(a - 3) ≥ 12 [9]
5.  b/2+b/3 > 7 [12] 
6.  (m - 3)/5 ≤ 1 [18]
7.  (3x + 4)/2 ≤ 1 [3] 
8.  3x - 7 ≠ 2x + 4 [2]

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Answer&Key

1) 6 is not a solution to the inequality.

Solution: From the questions x + 3 > 9,

by substituting x with 6,

we get 6 + 3 > 9.

Therefore, 9 > 9, which is false.

6 is then not a solution to the inequality x + 3 > 9.

2) -3 is a solution to the inequality.

Solution: From the questions 2x - 1 < 3,

by substituting x with -3,

we get 2(-3) - 1 < 3.

Therefore, -7 < 3, which is true.

-3 is then a solution to the inequality 2x - 1 < 3.

3) 5 is a solution to the inequality.

Solution: From the questions 7x + 4 > 18,

by substituting x with 5,

we get 7(5) + 4 > 18.

Therefore, 39 > 18, which is true.

5 is then a solution to the inequality 7x + 4 > 18.

4) 9 is a solution to the inequality.

Solution: From the questions 2(a - 3) ≥ 12,

by substituting a with 9,

we get 2(9 - 3) ≥ 12.

Therefore, 12 ≥ 12, which is true.

9 is then a solution to the inequality 2(a - 3) ≥ 12.

5) 12 is a solution to the inequality.

Solution: From the questions b/2+b/3 > 7,

by substituting b with 12,

we get 12/2 + 12/3 = 6 + 4 = 10.

Therefore, 10 > 7, which is true.

12 is then a solution to the inequality b/2 + b/3 > 7.

6) 18 is not a solution to the inequality.

Solution: From the questions (m - 3)/5 ≤ 1,

by substituting m with 18,

we get (18 - 3)/5 = 15/5 = 3.

Therefore, 3 ≤ 1, which is false.

18 is then not a solution to the inequality (m - 3)/5 ≤ 1.

7) 3 is not a solution to the inequality.

Solution: From the questions (3x + 4)/2 ≤ 1,

by substituting x with 3,

we get (3(3) + 4)/2 = 13/2 .

Therefore, 13/2 < 1, which is false.

3 is then not a solution to the inequality (3x + 4)/2 ≤ 1.

8) 2 is a solution to the inequality.

Solution: From the questions 3x - 7 ≠ 2x + 4,

by substituting x with 2,

we get 3(2) - 7 ≠ 2(2) + 4.

Therefore, -1 ≠ 8, which is true.

2 is then a solution to the inequality 3x - 7 ≠ 2x + 4.