Question

Solve (x + 5 < 4) ∩ (x - 3 > -6)

Answer 1

∅ i.e empty

Explanation:

(x + 5 < 4) ∩ (x - 3 > -6)

Let A represent the set (x + 5 < 4)

Let B represent the set (x - 3 > -6)

For set A:

x + 5 < 4

subtract 5 from both side

x < 4 —5

x < —9

Possible values of x are - 10, - 11, - 12,...

A = {- 10, - 11, - 12,...}

For set B:

x - 3 > -6

Add 3 to both side

x > -6 + 3

x > - 3

Possible values of x are - 2, - 1, 0,...

B = {- 2, - 1, 0,...}

A= {- 10, - 11, - 12,...}

A ∩ B = ∅ i.e empty

Therefore, (x + 5 < 4) ∩ (x - 3 > -6) is ∅ i.e empty