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Solve for x: −8 < x − 1 < 5

User H H
by
6.3k points

2 Answers

5 votes

Answer:

The solution is, x ∈ (-7, 6)

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)

User Behnam Rasooli
by
5.7k points
1 vote

Answer:

-7 < x < 6

Explanation:

Add 1 to all parts of the inequality:

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

-7 < x < 6

User Vretamal
by
6.2k points