SOLUTION: Rewrite each expression in a form that does not contain absolute values: (a) |pi - 4| + 1 (b) |x - 5| given that x <= 5 (c) |t - 5| given that t < 5. (d) |y +

(a)  The expression   = 3.14...-4  is negative,  --->  therefore  |pi-4| = 4 - ,
     by the definition of the absolute value expression.

     So, we write  |pi-4| + 1 =  = .    ANSWER



(b)  At x <= 5, the expression  x - 5  is negative or zero  --->  therefore  |x - 5| = 5 - x,
     by the definition of the absolute value expression.

     So, we write  |x - 5|  is  5 - x  at x <= 5.    ANSWER



(c)  At t < 5, the expression  t - 5  is negative  --->  therefore  |t - 5| = 5 - t,
     by the definition of the absolute value expression.

     So, we write  |t - 5|  =  5 - t  at  t < 5.    ANSWER



(d)  At y >= 15, the expression  y + 10  is positive  --->  therefore  |y + 10| = y + 10,
     by the definition of the absolute value expression.

     So, we write  |y + 10|  =  y + 10  at  y >= 15.    ANSWER

    the standard notation for the sign  " => "  (see your question 4)  is  " >= ".


    The sign  " => "  is your invention,  which is  NEVER  used in  Math.