y= |x−3| + |x+2| − |x−5|, if x>5 I need to know what y equals.

Question

y= |x−3| + |x+2| − |x−5|, if x>5
I need to know what y equals.

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Alexandra 2 weeks 2021-09-09T02:52:40+00:00 1 Answer 0

Answers ( )

    0
    2021-09-09T02:54:38+00:00

    Answer:

    y  \ge9

    Step-by-step explanation:

    The given function is

    y =  |x - 3|   +  |x  + 2|  -  |x - 5|

    By the triangle inequality property,

     |x + y|  \leqslant  |x|  +  |y|

    and the alternate triangle inequality property;

     |x - y|  \geqslant  |x|  -  |y|

    We apply this property to get:

    y  \geqslant   |x |    - |3|    +  |x |  +  |2|  -(  |x |  -  |5| )

    Expand parenthesis to get:

    y  \geqslant   |x |    - |3|    +  |x |  +  |2|  - |x |   +   |5|

    Simplify to get:

    y  \geqslant   |x |    - 3+  |x |  +  2- |x |   +   5

    Group similar terms to get:

    y  \geqslant   |x |  +   |x | - |x |    - 3 + 2+   5

    y  \geqslant   |x |   + 4

    When x>5,

    y  \geqslant   |5 |   + 4

    That’s;

    y  \geqslant   5  + 4   \\ y  \geqslant   9

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45:7+7-4:2-5:5*4+35:2 =? ( )