Solve The Inequality 47.75 + X ≤ 50 47.75 + X \leq 50 47.75 + X ≤ 50 To Determine How Much More Weight Can Be Added To Li's Suitcase Without Exceeding The 50-pound Limit. What Is The Solution Set?A. X ≤ 2.25 X \leq 2.25 X ≤ 2.25 B. X ≤ 2.75 X \leq 2.75 X ≤ 2.75 C. $x \geq

Introduction

In this article, we will delve into the world of inequalities and explore how to solve them. Specifically, we will tackle the inequality $47.75 + x \leq 50$ to determine how much more weight can be added to Li's suitcase without exceeding the 50-pound limit. We will break down the solution step by step, providing a clear understanding of the process and the final solution set.

What is an Inequality?

An inequality is a mathematical statement that compares two expressions using a relation such as greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤). Inequalities can be used to represent a wide range of real-world situations, from financial transactions to physical constraints.

The Inequality $47.75 + x \leq 50$

In this case, we are given the inequality $47.75 + x \leq 50$, which represents the weight limit of Li's suitcase. We want to find the maximum amount of weight that can be added to the suitcase without exceeding the 50-pound limit.

Step 1: Subtract 47.75 from Both Sides

To isolate the variable x, we need to get rid of the constant term 47.75 on the left-hand side of the inequality. We can do this by subtracting 47.75 from both sides of the inequality.

47.75 + x \leq 50
x \leq 50 - 47.75

Step 2: Simplify the Right-Hand Side

Now, we need to simplify the right-hand side of the inequality by performing the subtraction.

x \leq 2.25

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 $x \leq 2.25$. This means that the maximum amount of weight that can be added to Li's suitcase without exceeding the 50-pound limit is 2.25 pounds.

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 exceeding the 50-pound limit. We broke down the solution step by step, providing a clear understanding of the process and the final solution set. The solution set is $x \leq 2.25$, which represents the maximum amount of weight that can be added to the suitcase.

Common Mistakes to Avoid

When solving inequalities, it's essential to avoid common mistakes that can lead to incorrect solutions. Here are a few common mistakes to watch out for:

• Not following the order of operations: When solving inequalities, it's crucial to follow the order of operations (PEMDAS) to ensure that the correct operations are performed.
• Not considering the direction of the inequality: When solving inequalities, it's essential to consider the direction of the inequality (e.g., ≤, ≥, <, >) to ensure that the correct solution set is obtained.
• Not checking the solution set: When solving inequalities, it's crucial to check the solution set to ensure that it satisfies the original inequality.

Real-World Applications

Inequalities have numerous real-world applications, from finance to physics. Here are a few examples:

• Financial planning: Inequalities can be used to represent financial transactions, such as budgeting and saving.
• Physics: Inequalities can be used to represent physical constraints, such as the motion of objects and the behavior of systems.
• Engineering: Inequalities can be used to represent engineering constraints, such as the design of structures and the behavior of materials.

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 exceeding the 50-pound limit. We broke down the solution step by step, providing a clear understanding of the process and the final solution set. In this article, we will answer some frequently asked questions about solving inequalities.

Q: What is the difference between an inequality and an equation?

A: An equation is a statement that says two expressions are equal, while an inequality is a statement that compares two expressions using a relation such as greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤).

Q: How do I solve an inequality?

A: To solve an inequality, you need to isolate the variable on one side of the inequality sign. You can do this by adding or subtracting the same value to both sides of the inequality, or by multiplying or dividing both sides of the inequality by the same non-zero 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, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

Q: How do I handle inequalities with fractions?

A: When solving inequalities with fractions, you need to multiply or divide both sides of the inequality by the same non-zero value to eliminate the fraction. For example, if you have the inequality $\frac{x}{2} \leq 3$, you can multiply both sides of the inequality by 2 to get $x \leq 6$.

Q: Can I add or subtract the same value to both sides of an inequality?

A: Yes, you can add or subtract the same value to both sides of an inequality. For example, if you have the inequality $x + 2 \leq 5$, you can subtract 2 from both sides of the inequality to get $x \leq 3$.

Q: Can I multiply or divide both sides of an inequality by the same non-zero value?

A: Yes, you can multiply or divide both sides of an inequality by the same non-zero value. For example, if you have the inequality $x \leq 4$, you can multiply both sides of the inequality by 2 to get $2x \leq 8$.

Q: What is the solution set of an inequality?

A: The solution set of an inequality is the set of all values of the variable that satisfy the inequality. For example, if you have the inequality $x \leq 3$, the solution set is all values of x that are less than or equal to 3.

Q: How do I graph an inequality on a number line?

A: To graph an inequality on a number line, you need to plot a point on the number line that represents the solution set of the inequality. For example, if you have the inequality $x \leq 3$, you can plot a point on the number line at x = 3 and shade all values of x to the left of the point.

Conclusion

In this article, we answered some frequently asked questions about solving inequalities. We discussed the difference between an inequality and an equation, the order of operations for solving inequalities, and how to handle inequalities with fractions. We also covered how to add or subtract the same value to both sides of an inequality, how to multiply or divide both sides of an inequality by the same non-zero value, and how to graph an inequality on a number line.