Chapter 5.7, Problem 39E

To determine

To find: the system of linear inequalities that is equivalent to $\left|y\right|<x\text{}\text{ and }x>0$ and graph the system.

Answer to Problem 39E

Its equivalent to the $y<x\text{ and }y>-x$ and graph is plotted.

Explanation of Solution

Given:

  $\left|y\right|<x\text{}\text{ and }x>0$ .

Concept used:

Graphing the inequalities, it will graph the ordinary linear functions just like it is done before. The difference is that a solution to the inequality is not the drawn line but the area of the coordinate plane that satisfy the inequality. the boundary line is dashed for $<\text{or >}$ and solid line for $\le \text{or }\ge$ The common area is the solution of inequality.

There will be two signs for the domain inside the modulus.

If $\left|y\right|<x$ it implies:

  $y<x\text{ and }y>-x$ .

Calculation:

Write the system of linear inequalities that is equivalent to:

  $\left|y\right|<x$ .

Where $x>0$ .

Graph the system of linear inequalities.

The system of linear inequalities that is equivalent to:

  $\left|y\right|<x$ Where $x>0$ are:

  $y<x\text{ and }y>-x$ .

Graph the inequalities $y<x,y>-x\text{ and }x>0$ as shown in the below figure.

The graph of combination of $y<x,y>-x\text{ and }x>0$ is:

Hence, its equivalent to the $y<x\text{ and }y>-x$ and graph is plotted.