# To solve an equation involving an absolute value.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1, Problem 21RCC

a.

To determine

## To solve an equation involving an absolute value.

Expert Solution

The rules are described.

### Explanation of Solution

Given information:

How do you solve an equation involving an absolute value?

Calculation:

The absolute value of a number can be brought out as a distance on the number line from the origin.

An equality involving absolute value often get multiple solutions,

Absolute value of negative number is same as positive number (has same distance from the origin)

1. The equalities having absolute value isolate them on one side of the equation.
2. Then break up the equality into two equations. The first simply drops the absolute value. The second equation drops the absolute value but multiple the other side of the equality by a factor of 1 .
3. Then solve the equations.

Hence, the rules are described.

b.

To determine

### To solve an inequality involving an absolute value.

Expert Solution

The solution is 5<x<5 .

### Explanation of Solution

Given information:

How do you solve an inequality involving an absolute value?

Calculation:

The absolute value of a number can be brought out as a distance on the number line from the origin

The inequalities having absolute value isolate them on one side of the inequality.

Now write a double inequality for the variable to satisfy.

The first simply drops the absolute value. The second inequality drops the absolute value but reverses the inequality sign and by a factor of 1 .

Example, the given inequality;

|x5|<10

Break up this into the equivalent inequalities.

10<x5<10

The final step is to isolate the variables and then plot the solution to the inequality by adding 5 to both sides.

5<x<5

Hence, the solution is 5<x<5

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