Solve (x - 2 6).

A.) Ø

B.) x

C.) - 1 < x < 7

Option C:

{x: - 1 < x < 7}

Solution:

Given expression is (x - 2 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 6) = (x - 1)

= (x < 7) ∩ (-1 < x)

= - 1 < x < 7

Thus, option C is the correct answer.

(x - 2 6) = {x: - 1 < x < 7}