πŸ“’ Too many exams? Don’t know which one suits you best? Book Your Free Expert πŸ‘‰ call Now!

    Question

    Solve the inequality: (x βˆ’ 1)/(x + 2) > 2.

    Which of the following represents the solution set? (A) x < βˆ’5 (B) βˆ’5 < x < βˆ’2 (C) βˆ’2 < x < 1 (D) x > 1
    A A Correct Answer Incorrect Answer
    B B Correct Answer Incorrect Answer
    C C Correct Answer Incorrect Answer
    D D Correct Answer Incorrect Answer

    Solution

    ATQ, x β‰  βˆ’2. (x βˆ’ 1)/(x + 2) > 2 β‡’ (x βˆ’ 1)/(x + 2) βˆ’ 2 > 0 β‡’ (x βˆ’ 1 βˆ’ 2x βˆ’ 4)/(x + 2) > 0 β‡’ (βˆ’x βˆ’ 5)/(x + 2) > 0 Multiply numerator and denominator by βˆ’1 (reverses inequality): (x + 5)/(x + 2) < 0. Critical points: x = βˆ’5, x = βˆ’2. Sign analysis: For x < βˆ’5: numerator < 0, denominator < 0 β‡’ ratio > 0 (reject). For βˆ’5 < x < βˆ’2: numerator > 0, denominator < 0 β‡’ ratio < 0 (accept). For x > βˆ’2: numerator > 0, denominator > 0 β‡’ ratio > 0 (reject). Solution: βˆ’5 < x < βˆ’2.

    Practice Next
    More Algebra Questions
    ask-question