Determine If Each Value Of $X$ Is A Solution To The Inequality $46 \geq 35 + X$.$[ \begin{tabular}{|c|c|c|} \hline Value Of X X X & Is It A Solution? \ \hline 9 & Yes \ \hline 6 & Yes \ \hline 14 & No \ \hline 11 & No
Introduction
In mathematics, inequalities are a fundamental concept that helps us compare values and make decisions. In this article, we will focus on solving inequalities and determining if each value of X is a solution to the given inequality. We will use a step-by-step approach to understand the concept and apply it to real-world problems.
Understanding the Inequality
The given inequality is 46 ≥ 35 + x. To solve this inequality, we need to isolate the variable x. We can do this by subtracting 35 from both sides of the inequality.
Step 1: Subtract 35 from both sides
46 ≥ 35 + x 46 - 35 ≥ 35 + x - 35 11 ≥ x
Step 2: Determine the solution set
Now that we have isolated the variable x, we can determine the solution set. The solution set is the set of all values of x that satisfy the inequality. In this case, the solution set is all values of x that are less than or equal to 11.
Determining if each value of X is a solution
Now that we have the solution set, we can determine if each value of X is a solution to the inequality. We will use the following table to compare each value of X with the solution set.
| Value of X | Is it a solution? |
|---|---|
| 9 | Yes |
| 6 | Yes |
| 14 | No |
| 11 | No |
Discussion
Let's discuss each value of X and determine if it is a solution to the inequality.
- Value of X = 9: Since 9 is less than or equal to 11, it is a solution to the inequality.
- Value of X = 6: Since 6 is less than or equal to 11, it is a solution to the inequality.
- Value of X = 14: Since 14 is greater than 11, it is not a solution to the inequality.
- Value of X = 11: Since 11 is equal to 11, it is not a solution to the inequality.
Conclusion
In conclusion, we have solved the inequality 46 ≥ 35 + x and determined the solution set. We have also used the solution set to determine if each value of X is a solution to the inequality. By following the step-by-step approach, we can solve inequalities and make informed decisions.
Real-World Applications
Inequalities have many real-world applications. For example, in finance, inequalities can be used to determine the minimum amount of money needed to invest in a particular stock. In engineering, inequalities can be used to determine the maximum amount of stress that a material can withstand.
Tips and Tricks
Here are some tips and tricks to help you solve inequalities:
- Use the correct order of operations: When solving inequalities, make sure to follow the correct order of operations (PEMDAS).
- Isolate the variable: To solve an inequality, you need to isolate the variable. This can be done by adding or subtracting the same value from both sides of the inequality.
- Use the solution set: Once you have isolated the variable, you can use the solution set to determine if each value of X is a solution to the inequality.
Common Mistakes
Here are some common mistakes to avoid when solving inequalities:
- Not following the correct order of operations: Failing to follow the correct order of operations can lead to incorrect solutions.
- Not isolating the variable: Failing to isolate the variable can make it difficult to determine the solution set.
- Not using the solution set: Failing to use the solution set can lead to incorrect conclusions.
Conclusion
Introduction
In our previous article, we discussed how to solve inequalities and determine if each value of X is a solution to the given inequality. In this article, we will provide a Q&A guide to help you better understand the concept of solving inequalities.
Q: What is an inequality?
A: An inequality is a statement that compares two values using a mathematical symbol such as ≥, ≤, >, or <.
Q: How do I solve an inequality?
A: To solve an inequality, you need to isolate the variable by adding or subtracting the same value from both sides of the inequality.
Q: What is the solution set?
A: The solution set is the set of all values of the variable that satisfy the inequality.
Q: How do I determine if each value of X is a solution to the inequality?
A: To determine if each value of X is a solution to the inequality, you need to compare each value of X with the solution set.
Q: What are some common mistakes to avoid when solving inequalities?
A: Some common mistakes to avoid when solving inequalities include:
- Not following the correct order of operations
- Not isolating the variable
- Not using the solution set
Q: How do I apply inequalities to real-world problems?
A: Inequalities can be applied to many real-world problems, such as:
- Finance: Inequalities can be used to determine the minimum amount of money needed to invest in a particular stock.
- Engineering: Inequalities can be used to determine the maximum amount of stress that a material can withstand.
Q: What are some tips and tricks for solving inequalities?
A: Some tips and tricks for solving inequalities include:
- Using the correct order of operations
- Isolating the variable
- Using the solution set
Q: How do I know if I have solved the inequality correctly?
A: To know if you have solved the inequality correctly, you need to:
- Check if the solution set is correct
- Check if each value of X is a solution to the inequality
Q: What are some examples of inequalities?
A: Some examples of inequalities include:
- 2x + 3 ≥ 5
- x - 2 ≤ 3
- 4x > 12
Q: How do I graph an inequality?
A: To graph an inequality, you need to:
- Plot the boundary line
- Shade the region that satisfies the inequality
Q: What are some real-world applications of inequalities?
A: Some real-world applications of inequalities include:
- Finance: Inequalities can be used to determine the minimum amount of money needed to invest in a particular stock.
- Engineering: Inequalities can be used to determine the maximum amount of stress that a material can withstand.
- Science: Inequalities can be used to determine the maximum amount of a substance that can be present in a solution.
Conclusion
In conclusion, solving inequalities is a crucial skill that can be applied to many real-world problems. By following the step-by-step approach and using the correct order of operations, you can solve inequalities and make informed decisions. Remember to isolate the variable and use the solution set to determine if each value of X is a solution to the inequality.