Solve the following inequality which graph shows the correct solution – Inequalities are mathematical statements that compare two expressions using symbols such as >,<, ≥, and ≤. Solving inequalities involves finding the values of the variable that make the statement true. One method for solving inequalities is to graph them and determine the solution set visually.
This comprehensive guide will delve into the concept of graphing inequalities, exploring the different types of inequalities and providing step-by-step instructions on how to solve them using a graph. Additionally, we will discuss the practical applications of solving inequalities and how they can be used to solve real-world problems.
Solving Inequalities
Inequalities are mathematical statements that compare two expressions. They use symbols such as <, >, ≤, and ≥ to indicate the relationship between the expressions. Solving inequalities involves finding the values of the variable that make the inequality true.
There are different methods for solving inequalities, including:
- Graphing
- Using algebraic properties
- Using the substitution method
Graphing Inequalities
Graphing inequalities is a visual method for solving inequalities. It involves plotting the points that satisfy the inequality on a number line or in a coordinate plane.
The different types of inequalities are:
- Linear inequalities: These inequalities are represented by a straight line.
- Quadratic inequalities: These inequalities are represented by a parabola.
- Absolute value inequalities: These inequalities involve absolute values.
Solving Inequalities Using a Graph, Solve the following inequality which graph shows the correct solution
To solve an inequality using a graph, follow these steps:
- Graph the inequality.
- Identify the solution region, which is the region of the graph that satisfies the inequality.
- Write the solution set, which is the set of all values of the variable that satisfy the inequality.
Applications of Solving Inequalities
Solving inequalities has many applications in real-world problems. For example, inequalities can be used to:
- Determine the feasible region of a linear programming problem.
- Find the range of values for a variable that satisfy a given condition.
- Make decisions based on the results of an inequality.
FAQ Section: Solve The Following Inequality Which Graph Shows The Correct Solution
What is the difference between an equation and an inequality?
An equation is a mathematical statement that sets two expressions equal to each other, while an inequality compares two expressions using symbols such as >,<, ≥, and ≤.
How do I graph an inequality?
To graph an inequality, first draw the line or curve that represents the boundary of the inequality. Then, shade the region that satisfies the inequality.
How do I solve an inequality using a graph?
To solve an inequality using a graph, find the values of the variable that make the graph true. These values will be the solution set of the inequality.
