BuyFind

Single Variable Calculus: Concepts...

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

Single Variable Calculus: Concepts...

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

Solutions

Chapter A, Problem 15E
To determine

To solve the below inequality in terms of intervals and illustrate the solution set on the real number line -

  01x<1

Expert Solution

Answer to Problem 15E

The solution of the inequality is 0<x1 and the solution set on a real number line -

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter A, Problem 15E , additional homework tip  1

Explanation of Solution

Given: Inequality: 01x<1

Formula Used:

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.

Real number line is the line whose points are the real numbers. 

Calculation:

Given: Inequality equation is 01x<1

This inequality can be broken down into two inequalities:

  01x and 1x<1

Solving the firstinequality, we have:

Subtract (1) from both the sides -

  011x1

Solving further:

  1x

Divideboth the sides by (1) and reversing the inequality, we have:

  11x1

  1x ; i.e.:

  x1

Solving the second inequality, we have:

  1x<1

Subtract (1) from both the sides -

  1x1<11

Solving further:

  x<0

Multiplyboth the sides by (1) and reversing the inequality, we have:

  (x)×(1)>0×(1)

Solving further:

  x>0 ; i.e,

  0<x

Combining both the inequalities, we have:

  0<x1

Drawing the above inequality on a real number line, we have:

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter A, Problem 15E , additional homework tip  2

Conclusion:

Hence, the solution of the inequality is 0<x1 and the solution set on a real number line -

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter A, Problem 15E , additional homework tip  3

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