SOLUTION: 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 t

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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(52797)   (Show Source): You can put this solution on YOUR website!
.

For (a), the answer is   + 1 =  + 1 = .


For (b), |x-5| given that x >= 5  is x-5   (by the definition of the absolute value)


For (c), |t-5| given that t < 5  is -(t-5),  or  5-t.   (by the definition of the absolute value)

Solved, answered and explained, in full.

As a prerequisite, you must know/read/understand the definition of the absolute value.


=================


Comment from student : Good reply. For part (a), the book's answer is -pi + 5. Does it matter if I write it as you did: 5 - pi?


My response :   -pi+5 is the same  (is equal to)  5-pi.
It is as clear as a sunny day,  and any school student can confirm it . . .



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