Concept explainers
To calculate: The solution set of the given inequalities by graphing.
Answer to Problem 40STP
The solution set of the inequalities isan empty set.
Explanation of Solution
Given information:
The inequalities
Formula used:
To solve a system of inequalities by graphing, plot all the inequalities on the graph and shade the region that represents each inequality. The region that is common to all the inequalities i.e. shaded for all inequalities is the solution of the system.
Calculation:
Consider the given system of inequalities
Recall that to solve a system of inequalities by graphing, plot all the inequalities on the graph and shade the region that represents each inequality. The region that is common to all the inequalities i.e. shaded for all inequalities is the solution of the system.
To know whether the region will be shaded towards origin or away from the origin, substitute
Now, substitute
Since, the inequality is not true, so, its region will be shaded away from the origin as,
Now, substitute
Since, the inequality is true, so, its region will be shaded towards the origin as,
On combining both the inequalities on the graph, there is no common region to both the inequalities. So, there is no common point to both the inequalities.
In the above figure, there is no overlapping region for both the inequalities. Hence, there is no solution for the given set of inequalities.
Thus, the solution set of the inequalities is an empty set.
Chapter 3 Solutions
Algebra 2
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