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 25E
To determine

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

  1x<4

Expert Solution

Answer to Problem 25E

The solution of the inequality is x<0 or x>14 and the solution set on a real number line -

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter A, Problem 25E , additional homework tip  1

Explanation of Solution

Given: Inequality: 1x<4

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 1x<4

Subtracting 4 from both the sides, we have:

  1x4<441x4<014xx<0

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

When x<0 :

  x is negative and (14x) is positive

Thus, 14xx<0

So, x<0 isone of the solutions.

When 0<x<14 :

  x is positiveand (14x) is positive

Thus, 14xx>0

So, 0<x<14 is not one of the solutions.

When x>14 :

  x is negativeand (14x) is positive

Thus, 14xx<0

So, x>14 is one of the solutions.

Combining all the solutions, we have the solution set as:

  x<0 or x>14

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

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter A, Problem 25E , additional homework tip  2

Conclusion:

Hence, the solution of the inequality is x<0 or x>14 and the solution set on a real number line -

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter A, Problem 25E , additional homework tip  3

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