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Solve the inequality

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Solve the inequality. Write the solution in interval notation.
(x+14)/(x-8)≥ 1

  • Solve the inequality -

    if x-8> 0 , then
    x+14 ≥ x-8
    14 ≥ -8 , so true for all x's

    if x-8 < 0
    x+14 ≤ x-8
    14 ≤ -8 , no way!

    so true for x > 8

    check:
    take a value > 8
    e.g. x = 10
    statement becomes
    24/2 ≥ 1 , true

    take a value < 8
    e.g
    x = 1
    statement becomes
    15/-7≥1 , false
    how about x = -20
    statement becomes
    -6/-28 ≥ 1 or 3/14 ≥ 1 false

    solution x > 8

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