Question 1207367: Rewrite each expression in a form that does not contain absolute values:
(a) |pi - 4| + 1
I know that the quantity pi - 4 is negative. So, -(pi - 4) = -pi + 4.
Is this right?
I need help with (b) and (c).
(b) |x - 5|, given that x > or = 5
(c) |t - 5|, given that t < 5.
Note: The book tells me to use the formal definition of absolute value.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Rewrite each expression in a form that does not contain absolute values:
(a) |pi - 4| + 1
I know that the quantity pi - 4 is negative. So, -(pi - 4) = -pi + 4.
Is this right?
It's right as far as you have gone; but you haven't rewritten the entire given expression. pi is less than 4, so pi-4 is negative, so |pi-4| = 4-pi. Then the whole given expression is equivalent to (4-pi)+1 = 5-pi.
I need help with (b) and (c).
(b) |x - 5|, given that x > or = 5
If x >= 5, then x-5 is non-negative, so |x-5| = x-5
(c) |t - 5|, given that t < 5.
If t < 5, then t-5 is negative, so |t-5| = -(t-5) = 5-t (similar to what you did in (a))
Note: The book tells me to use the formal definition of absolute value.
Answer by ikleyn(52794)  (Show Source):
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