Solve The Inequality $47.75 + X \leq 50$ To Determine How Much More Weight Can Be Added To Li's Suitcase Without Going Over The 50-pound Limit. What Is The Solution Set?A. $x \leq 2.25$ B. \$x \leq 2.75$[/tex\] C.
Introduction
Inequality problems are a crucial part of mathematics, and they often involve real-world applications. One such application is determining weight limits, such as the 50-pound limit for Li's suitcase. In this article, we will solve the inequality $47.75 + x \leq 50$ to determine how much more weight can be added to Li's suitcase without going over the 50-pound limit.
Understanding the Problem
The given inequality is $47.75 + x \leq 50$. This means that the weight of Li's suitcase, including the additional weight, must not exceed 50 pounds. To solve this inequality, we need to isolate the variable x, which represents the additional weight that can be added to the suitcase.
Step 1: Subtract 47.75 from Both Sides
To isolate the variable x, we need to subtract 47.75 from both sides of the inequality. This will give us the following result:
Step 2: Simplify the Right-Hand Side
Now, we need to simplify the right-hand side of the inequality by performing the subtraction:
Step 3: Write the Solution Set
The solution set is the set of all possible values of x that satisfy the inequality. In this case, the solution set is $x \leq 2.25$. This means that the additional weight that can be added to Li's suitcase without going over the 50-pound limit is 2.25 pounds or less.
Conclusion
In this article, we solved the inequality $47.75 + x \leq 50$ to determine how much more weight can be added to Li's suitcase without going over the 50-pound limit. The solution set is $x \leq 2.25$, which means that the additional weight that can be added to Li's suitcase is 2.25 pounds or less.
Comparison of Solution Sets
Now, let's compare the solution set we obtained with the given options:
- Option A: $x \leq 2.25$
- Option B: $x \leq 2.75$
- Option C: (not provided)
Our solution set matches option A, which is $x \leq 2.25$. This means that the correct answer is option A.
Real-World Applications
Inequality problems like this one have many real-world applications. For example, in the context of travel, understanding weight limits is crucial to avoid additional fees or even being denied boarding. In the context of business, understanding weight limits can help companies optimize their shipping processes and reduce costs.
Tips and Tricks
When solving inequality problems, it's essential to follow the order of operations and to isolate the variable on one side of the inequality. Additionally, make sure to simplify the right-hand side of the inequality to obtain the solution set.
Conclusion
Introduction
In our previous article, we solved the inequality $47.75 + x \leq 50$ to determine how much more weight can be added to Li's suitcase without going over the 50-pound limit. In this article, we will provide a Q&A guide to help you better understand solving inequalities.
Q: What is an inequality?
A: An inequality is a mathematical statement that compares two expressions using a relation such as <, >, ≤, or ≥.
Q: What is the difference between an inequality and an equation?
A: An equation is a mathematical statement that states that two expressions are equal, whereas an inequality is a mathematical statement that compares two expressions using a relation such as <, >, ≤, or ≥.
Q: How do I solve an inequality?
A: To solve an inequality, you need to isolate the variable on one side of the inequality. This can be done by adding, subtracting, multiplying, or dividing both sides of the inequality by the same value.
Q: What is the order of operations for solving inequalities?
A: The order of operations for solving inequalities is the same as for solving equations:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I handle negative numbers when solving inequalities?
A: When solving inequalities, you need to be careful when handling negative numbers. If you multiply or divide both sides of the inequality by a negative number, you need to reverse the direction of the inequality.
Q: What is the solution set of an inequality?
A: The solution set of an inequality is the set of all possible values of the variable that satisfy the inequality.
Q: How do I write the solution set of an inequality?
A: To write the solution set of an inequality, you need to use interval notation. For example, if the solution set is all real numbers less than or equal to 2, you would write it as (-∞, 2].
Q: What are some common mistakes to avoid when solving inequalities?
A: Some common mistakes to avoid when solving inequalities include:
- Not following the order of operations
- Not isolating the variable on one side of the inequality
- Not reversing the direction of the inequality when multiplying or dividing by a negative number
- Not using interval notation to write the solution set
Q: How do I check my solution to an inequality?
A: To check your solution to an inequality, you need to plug in a value from the solution set into the original inequality and verify that it is true.
Conclusion
In conclusion, solving inequalities is a crucial part of mathematics, and it has many real-world applications. In this article, we provided a Q&A guide to help you better understand solving inequalities. By following the order of operations, isolating the variable, and using interval notation, you can solve inequalities with confidence.
Tips and Tricks
- Make sure to follow the order of operations when solving inequalities.
- Isolate the variable on one side of the inequality.
- Use interval notation to write the solution set.
- Check your solution to an inequality by plugging in a value from the solution set.
Real-World Applications
Inequality problems like this one have many real-world applications. For example, in the context of travel, understanding weight limits is crucial to avoid additional fees or even being denied boarding. In the context of business, understanding weight limits can help companies optimize their shipping processes and reduce costs.
Conclusion
In conclusion, solving inequalities is a crucial part of mathematics, and it has many real-world applications. By following the order of operations, isolating the variable, and using interval notation, you can solve inequalities with confidence.