# To rewrite: The expression without the absolute value symbol. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter A, Problem 10E
To determine

## To rewrite: The expression without the absolute value symbol.

Expert Solution

The equivalent form of the given expression is {12x2     if 12x122x21   if x<12 or x>12.

### Explanation of Solution

Given:

The expression is |12x2|.

Definition used:

The absolute value of a number a, denoted by |a|, is the distance from a to 0 on the real

number line. Distances are always positive or 0, so |a|0 and {|a|=a    if a0|a|=a  if a<0.

Calculation:

Solve the above expression as,

12x2<01<2x212<x2x2>12

Take square root on both sides,

x2>12x>12|x|>12

The expression can be re written as,

x>12 orx<12

Thus, the expression becomes,

|12x2|={12x2     if 12x122x21   if x<12 or x>12

Hence, the equivalent form of the given expression is {12x2     if 12x122x21   if x<12 or x>12.

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