Solve for x: - 8 < x - 1 < 5

The solution is, x ∈ (-7, 6)

Step-by-step explanation:

Given compound inequality,

-8 < x - 1 < 5

⇒ - 8 < x - 1 and x - 1 < 5

⇒ - 8 + 1 < x and x < 5 + 1 (a < b, a - c < b - c ∀ a, b, c ∈ R)

⇒ - 7 < x and x < 6

⇒ x is all real numbers greater than - 7 and less than 6.

⇒ x ∈ (-7, ∞) and x ∈ (-∞, 6)

⇒ x ∈ (-7, ∞) ∩ (-∞, 6)

⇒ x ∈ (-7, 6)

-7 < x < 6

Step-by-step explanation:

Add 1 to all parts of the inequality:

-8 + 1 < x - 1 + 1 < 5 + 1

-7 < x < 6