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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 + 10| given that y => 15
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(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
Solved. I answered all question.
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For your info
the standard notation for the sign " => " (see your question 4) is " >= ".
The sign " => " is your invention, which is NEVER used in Math.