PRECALCULUS:GRAPHICAL,...-W/ACCESS
PRECALCULUS:GRAPHICAL,...-W/ACCESS
10th Edition
ISBN: 9780134781945
Author: Demana
Publisher: PEARSON
Expert Solution & Answer
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Chapter P.2, Problem 51E
Solution

Write the given statement using absolute value notation.

  x−c<d

Given information:

Statement is:

“The distance between x and c is less than d units.”

Formula used:

  1. Absolute value is representation on either side of the expression given by two parallel line.

    2. Absolute value x means:

      x=x if x is positive−x if x is negative

    For example, if the distance between x and y is a this is represented by absolute value notation as:

      x−y=a

  2. a less than b is represented as:

    3.   a<b

Calculation:

To write the given statement using absolute value notation first note that for any x :

  x=x if x is positive−x if x is negative

Now, note that the distance between x and y is a this is represented by absolute value notation as:

  x−y=a

Here, the given statement is:

“The distance between x and c is less than d units.”

First note that the distance between x and c is represented as:

  x−c, or −x−c

It’s absolute notation is:

  x−c

Now since the representation of a less than b is represented as:

  a<b

Thus, distance between x and c is less than d units in absolute value notation is represented by:

  x−c<d

Thus, the absolute value notation of the given statement is:

  x−c<d

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Chapter P.2, Problem 50E
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Chapter P.2, Problem 52E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-W/ACCESS

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