# 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 8E
To determine

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

Expert Solution

The equivalent form of the given expression is {(2x1)      if x12(2x1)   if x<12.

### Explanation of Solution

Given:

The expression is |2x1|.

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:

In the definition of absolute value, substitute a=2x1.

|2x1|={(2x1)      if 2x10(2x1)   if 2x1<0

Solve the above expression as,

2x1=02x=1x=12

Thus, the expression becomes,

|2x1|={(2x1)      if x12(2x1)   if x<12

Hence, the equivalent form of the given expression is {(2x1)      if x12(2x1)   if x<12.

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