2022 AMC 10 A

Complete problem set with solutions and individual problem pages

Problem 6 Easy

Which expression is equal to \left| a-2-\sqrt{(a-1)^{2}}\right| for a\lt0?

  • A.

    3-2a

  • B.

    1-a

  • C.

    1

  • D.

    a+1

  • E.

    3

Answer:A
Solution

\because a<0

\therefore |a-2-\sqrt{(a-1)^2}|=|a-2-(1-a)|=|2a-3|=3-2a.

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