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           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality 1 ≥arccos（2x-3） ≥-1 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 2 inequalities：
        1 ≥ arccos ( 2 * x - 3 )         (1)
         arccos ( 2 * x - 3 ) ≥ -1         (2)
        From the definition field of arccos
         2 * x - 3 ≥ -1        (3 )
         2 * x - 3 ≤ 1        (4 )

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    From inequality(1)：
         x ≤ 1 或  x ≥ 1.770151
    From inequality(2)：
         x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
    From inequality(3)：
         x ≥ 1
    From inequality(4)：
         x ≤ 2

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    From inequalities (1) and (2)
         x ≤ 1 或  x ≥ 1.770151    (5)
    From inequalities (3) and (5)
         1 ≤ x ≤ 1 或  x ≥ 1.770151    (6)
    From inequalities (4) and (6)
         1 ≤ x ≤ 1 或  1.770151 ≤ x ≤ 2    (7)

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    The final solution set is :
         1 ≤ x ≤ 1 或  1.770151 ≤ x ≤ 2

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