Question

The members of set A are the integer solutions of the inequality 2x−5≤11 and the members of set B are the integer solutions of the inequality −2x+7≤−9. What is one member of the intersection of A and B?

Answer 1

The members of set A are the integer solutions of the inequality : 2x - 5 ≤ 11
or, 2x ≤ 11 + 5
or, 2x ≤ 16
or, x ≤ 8
or , x belongs to (-∞ , 8)

and the members of set B are the integer solutions of the inequality : -2x + 7 ≤ -9
or, -2x ≤ -9 - 7
or, -2x ≤ -16
or, 2x ≥ 16
or, x ≥ 8
or, x belongs to (8, ∞ )

so, A intersection B = common value of A and B = 8
hence, answer is x = 8

Answer 2

Given:

Set A inequality: 2x - 5 ≤ 11

Set B inequality: -2x + 7 ≤ -9

Solution:

To find the integers in the sets,

Solve the inequality,

Set A:

2x - 5 ≤ 11

2x ≤ 11 + 5

2x ≤ 16

x ≤ 8

Therefore,

The x in set A contains 8, 7, 6, ...

Set B:

2x + 7 ≤ -9

-2x ≤ -9 - 7

-2x ≤ -16

2x ≥ 16

x ≥ 8

Therefore,

The x in set B contains 8, 9, 10, 11, ...

Intersection: Common integer belonging to both the sets.

So, the one member of the intersection of A and B is 8.

The answer is integer 8.