Which Of The Following Is The Correct Solution To The Linear Inequality Shown Below?$y \ \textless \ \frac{1}{2} X - 4$A. B.
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Introduction
Linear inequalities are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will explore the correct solution to a linear inequality and provide a step-by-step guide on how to solve it.
Understanding Linear Inequalities
A linear inequality is an inequality that involves a linear expression. It is a mathematical statement that compares two expressions, and the result is either greater than, less than, greater than or equal to, or less than or equal to. In this case, we have the linear inequality .
The Correct Solution
To solve the linear inequality , we need to isolate the variable . We can do this by adding to both sides of the inequality, which gives us . Then, we can subtract from both sides to get . Finally, we can subtract from both sides to get .
Graphing the Solution
To graph the solution, we need to find the boundary line of the inequality. The boundary line is the line that separates the region where the inequality is true from the region where it is false. In this case, the boundary line is the line . We can graph this line by plotting two points on the line and drawing a line through them.
Finding the Solution Region
To find the solution region, we need to determine which side of the boundary line the inequality is true. We can do this by testing a point on each side of the line. If the point satisfies the inequality, then the region on that side of the line is the solution region.
Conclusion
In conclusion, the correct solution to the linear inequality is . We can graph the solution by finding the boundary line and determining which side of the line the inequality is true. By following these steps, we can solve linear inequalities and find the solution region.
Frequently Asked Questions
Q: What is a linear inequality?
A: A linear inequality is an inequality that involves a linear expression.
Q: How do I solve a linear inequality?
A: To solve a linear inequality, you need to isolate the variable by adding or subtracting the same value from both sides of the inequality.
Q: What is the boundary line of a linear inequality?
A: The boundary line of a linear inequality is the line that separates the region where the inequality is true from the region where it is false.
Q: How do I graph the solution to a linear inequality?
A: To graph the solution, you need to find the boundary line and determine which side of the line the inequality is true.
Final Answer
The final answer is:
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Introduction
Linear inequalities are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will provide a comprehensive Q&A guide on linear inequalities, covering various topics and concepts.
Q&A: Linear Inequalities
Q: What is a linear inequality?
A: A linear inequality is an inequality that involves a linear expression. It is a mathematical statement that compares two expressions, and the result is either greater than, less than, greater than or equal to, or less than or equal to.
Q: How do I solve a linear inequality?
A: To solve a linear inequality, you need to isolate the variable by adding or subtracting the same value from both sides of the inequality. You can also multiply or divide both sides of the inequality by a non-zero value, but be careful not to change the direction of the inequality.
Q: What is the boundary line of a linear inequality?
A: The boundary line of a linear inequality is the line that separates the region where the inequality is true from the region where it is false. The boundary line is the line that is equal to the expression on one side of the inequality.
Q: How do I graph the solution to a linear inequality?
A: To graph the solution, you need to find the boundary line and determine which side of the line the inequality is true. You can test a point on each side of the line to determine which side is the solution region.
Q: What is the difference between a linear inequality and a linear equation?
A: A linear equation is an equation that involves a linear expression, and the result is equal to zero. A linear inequality, on the other hand, is an inequality that involves a linear expression, and the result is either greater than, less than, greater than or equal to, or less than or equal to.
Q: Can I multiply or divide both sides of a linear inequality by a negative value?
A: No, you cannot multiply or divide both sides of a linear inequality by a negative value. This will change the direction of the inequality, which can lead to incorrect solutions.
Q: How do I solve a linear inequality with fractions?
A: To solve a linear inequality with fractions, you need to eliminate the fractions by multiplying both sides of the inequality by the least common multiple (LCM) of the denominators.
Q: Can I use a calculator to solve a linear inequality?
A: Yes, you can use a calculator to solve a linear inequality, but be careful not to make any mistakes. Make sure to check your work and verify that the solution is correct.
Advanced Q&A: Linear Inequalities
Q: How do I solve a linear inequality with absolute values?
A: To solve a linear inequality with absolute values, you need to consider two cases: when the expression inside the absolute value is positive, and when it is negative. You can then solve each case separately and combine the solutions.
Q: How do I solve a linear inequality with multiple variables?
A: To solve a linear inequality with multiple variables, you need to isolate one variable by adding or subtracting the same value from both sides of the inequality. You can then solve for the other variables using substitution or elimination methods.
Q: Can I use a graphing calculator to solve a linear inequality?
A: Yes, you can use a graphing calculator to solve a linear inequality. You can graph the boundary line and determine which side of the line the inequality is true.
Conclusion
In conclusion, linear inequalities are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. By following the steps outlined in this Q&A guide, you can solve linear inequalities and understand the concepts and techniques involved.
Final Answer
The final answer is: There is no final answer, as this is a Q&A guide.