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Question

If   vertical line 2 x plus 3 vertical line equals 5and vertical line 3 y minus 3 vertical line equals 6 , what is one possible value of  vertical line x y vertical line ?

hintHint:

Hint:
vertical line x vertical line is called the absolute value of x . The value of the expression is given as
vertical line x vertical line equals open curly brackets table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell negative x comma x less than 0 end cell row cell x comma x greater or equal than 0 end cell end table close
To find the value of vertical line x y vertical line , we first find value of x and y  seperately, and then find absolute value of their product. There can be four different cases here, two cases for each equation. We will take the case where both the values are positive.

The correct answer is: 1,3,4,12


    We are given two equations vertical line 2 x plus 3 vertical line equals 5and vertical line 3 y minus 3 vertical line equals 6
    To find: vertical line x y vertical line
    Considering, the first equation, we have
    vertical line 2 x plus 3 vertical line equals 5
    As this is true for all values of x ,
    We take  such that 2 x plus 3 greater than 0 not stretchy rightwards double arrow x greater than negative 3 over 2
    Then
    vertical line 2 x plus 3 vertical line equals 2 x plus 3 ∣
    Thus, we get
    2 x plus 3 equals 5
    Solving this equation, we have
    2 x equals 5 minus 3 equals 2
    not stretchy rightwards double arrow x equals 1
    Next, consider the equation
    vertical line 3 y minus 3 vertical line equals 6 ∣
    As this is true for all values of y ,
    W e space t a k e space y space s u c h space t h a t space 3 y minus 3 greater than 0 rightwards double arrow y greater than 1 space T h e n
    vertical line 3 y minus 3 vertical line equals 3 y minus 3
    So, we have
    Solving this equation for y , we have
    3 y equals 6 plus 3 equals 9
    not stretchy rightwards double arrow y equals 3
    Thus, we get values of x and  y as
    x equals 1 comma y equals 3
    From here, we have,
    x y equals 3 cross times 1 equals 3
    As 3 greater than 0 so by definition, we get vertical line x y vertical line equals x y equals 3
    Therefore, one possible value of vertical line x y vertical line is 3.

    Note:
    This problem can have different answers if solved differently. Instead of making  2 x plus 3 positive, if we took 2 x plus 3 less than 0 , we would get a different answer. Similarly,3 y minus 3 less than 0  for  , we get a different value of  vertical line x y vertical line. If we take both negative, we will get another answer.
    Thus, we can get 4 answers: 1,3, 4, 12.

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