Question

Solve (x + 2 < 5) ∩ (x - 7 > -6).
o {x | 1 < x < 3}
o {x | x < 3 or x > 1}
o {all real numbers}

Answer 1

(x + 2 < 5) ∩ (x - 7 > -6 )

first solve x + 2 < 5.
this is based on concept of inequality.
so, x + 2 < 5
x < 5 - 2
x < 3 , e.g., x is set of all real numbers less than 3.

again solve x - 7 > -6
so, x - 7 > -6
x > -6 - (-7)
x > -6 + 7
x > 1, e.g., x is set of all real numbers greater than 1.

now we have to find intersection of (x + 2< 5) and (x - 7 > -6)
or, we have to find common value of x < 3 and x > 1

so, common set of x < 3 and x > 1 is 1 < x < 3

e.g., answer is 1 < x < 3.

first option is correct.

Answer 2

Answer:

{x / 1 < x < 3 }

Step-by-step explanation:

In the attachment I have answered this problem.

See the attachment for detailed solution.

I hope this answer helps you