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5 November, 06:06

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

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Answers (2)
  1. 5 November, 06:43
    0
    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)
  2. 5 November, 07:25
    0
    -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
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