Question

Solve (x - 2 < 5) ∩ (x + 7 > 6).
A.) Ø
B.) {x | x < -1 U x < 7}
C.) {x | -1 < x < 7}

Answer 1

Option C:

{x: –1 < x < 7}

Solution:

Given expression is  (x – 2 < 5) ∩ (x + 7 > 6).

Let us first solve the inequality.

First inequality:

⇒ x – 2 < 5

Add 2 on both sides of the expression.

⇒ x – 2 + 2 < 5 + 2

⇒ x < 7

Second inequality:

⇒ x + 7 > 6

Subtract 7 on both sides of the expression.

⇒ x + 7 – 7 > 6 – 7

⇒ x + 7 – 7 > 6 – 7

⇒ x > –1

Now to find the intersection of these inequalities.

(x – 2 < 5) ∩ (x + 7 > 6) = (x < 7) ∩ (x > –1)

                                     = (x < 7) ∩ (–1 < x)

                                     = –1 < x < 7

Thus, option C is the correct answer.

(x – 2 < 5) ∩ (x + 7 > 6) = {x: –1 < x < 7}