Which graph represents the solution set of the compound inequality – In the realm of mathematics, the notion of compound inequalities plays a pivotal role in defining constraints and relationships within a given problem. Which graph represents the solution set of a compound inequality is a question that delves into the heart of this concept, enabling us to visualize and comprehend the intricate interplay of these mathematical expressions.

Compound inequalities, characterized by the presence of multiple inequalities joined by logical operators (and/or), present a unique challenge in determining the set of values that satisfy all the inequalities simultaneously. The solution set, represented graphically, provides a powerful tool for understanding the constraints and relationships involved, making it an essential skill in various fields, including science, engineering, and economics.

Compound Inequality

A compound inequality is a mathematical statement that contains two or more inequalities joined by the word “and” or “or”. For example, the inequality x > 3 and x< 5 is a compound inequality.

Types of Compound Inequalities, Which graph represents the solution set of the compound inequality

• Conjunctive Compound Inequality:A compound inequality joined by the word “and” is called a conjunctive compound inequality. The solution set of a conjunctive compound inequality is the intersection of the solution sets of the individual inequalities.
• Disjunctive Compound Inequality:A compound inequality joined by the word “or” is called a disjunctive compound inequality. The solution set of a disjunctive compound inequality is the union of the solution sets of the individual inequalities.

Solution Set of a Compound Inequality

The solution set of a compound inequality is the set of all values of the variable that satisfy the inequality. To find the solution set of a compound inequality, we need to solve each individual inequality and then combine the solution sets according to the type of compound inequality.

Step-by-Step Procedure for Finding the Solution Set of a Compound Inequality

1. Solve each individual inequality.
2. If the compound inequality is conjunctive, find the intersection of the solution sets of the individual inequalities.
3. If the compound inequality is disjunctive, find the union of the solution sets of the individual inequalities.

Graphing the Solution Set of a Compound Inequality

To graph the solution set of a compound inequality, we can use a number line, interval notation, or a graph of the inequality.

Step-by-Step Procedure for Graphing the Solution Set of a Compound Inequality

1. Solve the compound inequality to find the solution set.
2. If the solution set is an interval, plot the interval on a number line or write it in interval notation.
3. If the solution set is a union of intervals, plot each interval on a number line or write it in interval notation.

Examples of Graphing the Solution Set of a Compound Inequality: Which Graph Represents The Solution Set Of The Compound Inequality

Here are some examples of compound inequalities and their corresponding graphs:

• Conjunctive Compound Inequality:x > 3 and x < 5 Solution set: (3, 5) Graph: A shaded region on a number line between 3 and 5, excluding the endpoints.
• Disjunctive Compound Inequality:x ≤ 2 or x ≥ 4 Solution set: (-∞, 2] ∪ [4, ∞) Graph: Two shaded regions on a number line, one from negative infinity to 2, and the other from 4 to positive infinity.

Applications of Graphing the Solution Set of a Compound Inequality

Graphing the solution set of a compound inequality can be useful in a variety of applications, including:

• Solving problems in science:For example, a scientist might use a compound inequality to find the range of temperatures at which a chemical reaction will occur.
• Solving problems in engineering:For example, an engineer might use a compound inequality to find the range of loads that a bridge can safely support.
• Solving problems in economics:For example, an economist might use a compound inequality to find the range of prices at which a product will be in demand.

Popular Questions

What is a compound inequality?

A compound inequality is an inequality that contains two or more inequalities joined by the logical operators “and” or “or”.

How do you find the solution set of a compound inequality?

To find the solution set of a compound inequality, you need to solve each inequality separately and then find the intersection or union of the solution sets, depending on whether the inequalities are joined by “and” or “or”.

How do you graph the solution set of a compound inequality?

To graph the solution set of a compound inequality, you can use a number line or interval notation. On a number line, the solution set is represented by the points that satisfy all the inequalities in the compound inequality. In interval notation, the solution set is represented by the set of all intervals that satisfy all the inequalities in the compound inequality.