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 21E
To determine

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

  x3x20

Expert Solution

Answer to Problem 21E

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

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter A, Problem 21E , additional homework tip  1

Explanation of Solution

Given: Inequality: x3x20

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 x3x20

Simplifying the above inequality, we have:

  x3x20

  x2(x1)0

To solve the above inequalities, we need to find the different intervals for which the inequality gives a value less than or equal to 0 .

When x<0 :

  x is Zero and (x1) is negative.

Thus, x2(x1)<0

So, x<0 is one of the solutions.

When x=0 :

  x is Zero and (x1) is negative.

Thus, x2(x1)=0

So, x=0 is one of the solutions.

When 0<x<1 :

  x is positive and (x1) is negative.

Thus, x2(x1)<0

So, 0<x<1 is one of the solutions.

When x=1 :

  x is positive and (x1) is Zero.

Thus, x2(x1)=0

So, x=1 is one of the solutions.

When x>1 :

  x is positive and (x1) is positive.

Thus, x2(x1)>0

So, x>1 is not one of the solutions.

Combining all the solutions, we have:

  x<0 or x=0 or 0<x<1 or x=1

Thus, the solution is x1

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

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter A, Problem 21E , additional homework tip  2

Conclusion:

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

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter A, Problem 21E , additional homework tip  3

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