Choose The Correct Inequality That Represents The Expression 3 X ≤ 12 3x \leq 12 3 X ≤ 12 .A. X ≤ 3 X \leq 3 X ≤ 3 B. X ≤ 4 X \leq 4 X ≤ 4 C. X ≤ 12 X \leq 12 X ≤ 12 D. X ≤ 24 X \leq 24 X ≤ 24

Introduction

Inequalities are mathematical expressions that compare two values or expressions using greater than, less than, greater than or equal to, or less than or equal to symbols. Solving inequalities involves isolating the variable on one side of the inequality sign. In this article, we will focus on solving the inequality $3x \leq 12$ and choose the correct inequality that represents the expression.

Understanding the Inequality

The given inequality is $3x \leq 12$. This means that the product of 3 and x is less than or equal to 12. To solve this inequality, we need to isolate the variable x.

Step 1: Divide Both Sides by 3

To isolate x, we need to get rid of the coefficient 3. We can do this by dividing both sides of the inequality by 3.

$$\frac{3x}{3} \leq \frac{12}{3}$$

This simplifies to:

$$x \leq 4$$

Step 2: Check the Solution

To check our solution, we can plug in a value of x that satisfies the inequality. Let's say x = 4. Plugging this value into the original inequality, we get:

$$3(4) \leq 12$$

$$12 \leq 12$$

This is true, so our solution is correct.

Choosing the Correct Inequality

Now that we have solved the inequality, we need to choose the correct inequality that represents the expression $3x \leq 12$. Let's look at the options:

A. $x \leq 3$ B. $x \leq 4$ C. $x \leq 12$ D. $x \leq 24$

Based on our solution, we know that x is less than or equal to 4. Therefore, the correct inequality is:

B. $x \leq 4$

Conclusion

Solving inequalities involves isolating the variable on one side of the inequality sign. In this article, we solved the inequality $3x \leq 12$ and chose the correct inequality that represents the expression. We divided both sides of the inequality by 3 to isolate x and checked our solution by plugging in a value of x that satisfies the inequality. Our solution was $x \leq 4$, which is the correct inequality that represents the expression $3x \leq 12$.

Common Mistakes to Avoid

When solving inequalities, it's easy to make mistakes. Here are some common mistakes to avoid:

• Not checking the solution: Make sure to check your solution by plugging in a value of x that satisfies the inequality.
• Not isolating the variable: Make sure to isolate the variable on one side of the inequality sign.
• Not considering the direction of the inequality: Make sure to consider the direction of the inequality sign when solving the inequality.

Real-World Applications

Inequalities have many real-world applications. Here are a few examples:

• Finance: Inequalities are used to calculate interest rates and investment returns.
• Science: Inequalities are used to model population growth and chemical reactions.
• Engineering: Inequalities are used to design and optimize systems.

Practice Problems

Here are a few practice problems to help you practice solving inequalities:

• Problem 1: Solve the inequality $2x \geq 10$.
• Problem 2: Solve the inequality $x - 3 \leq 5$.
• Problem 3: Solve the inequality $3x - 2 \geq 11$.

Answer Key

Here are the answers to the practice problems:

• Problem 1: $x \geq 5$
• Problem 2: $x \leq 8$
• Problem 3: $x \geq 3.67$

Conclusion

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Introduction

In our previous article, we discussed how to solve the inequality $3x \leq 12$ and chose the correct inequality that represents the expression. In this article, we will provide a Q&A guide to help you understand and solve inequalities.

Q: What is an inequality?

A: An inequality is a mathematical expression that compares two values or expressions using greater than, less than, greater than or equal to, or less than or equal to symbols.

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, subtracting, multiplying, or dividing both sides of the inequality by the same value.

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

A: An equation is a mathematical expression that states that two values or expressions are equal. An inequality, on the other hand, states that one value or expression is greater than, less than, greater than or equal to, or less than or equal to another value or expression.

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 of x that satisfies the inequality and see if it is true. If it is true, then your solution is correct.

Q: What are some common mistakes to avoid when solving inequalities?

A: Some common mistakes to avoid when solving inequalities include:

• Not checking the solution
• Not isolating the variable
• Not considering the direction of the inequality
• Not using the correct operations (e.g. adding, subtracting, multiplying, or dividing)

Q: How do I use inequalities in real-world applications?

A: Inequalities have many real-world applications, including:

• Finance: Inequalities are used to calculate interest rates and investment returns.
• Science: Inequalities are used to model population growth and chemical reactions.
• Engineering: Inequalities are used to design and optimize systems.

Q: What are some examples of inequalities in real-world applications?

A: Some examples of inequalities in real-world applications include:

• A company's profit is greater than or equal to $100,000 per year.
• A population of bacteria grows at a rate of 20% per day, and the initial population is 100.
• A car's speed is less than or equal to 60 miles per hour.

Q: How do I solve inequalities with fractions?

A: To solve inequalities with fractions, you need to follow the same steps as solving inequalities with whole numbers. However, you may need to multiply both sides of the inequality by the denominator to eliminate the fraction.

Q: How do I solve inequalities with decimals?

A: To solve inequalities with decimals, you need to follow the same steps as solving inequalities with whole numbers. However, you may need to multiply both sides of the inequality by 10 to eliminate the decimal.

Q: What are some tips for solving inequalities?

A: Some tips for solving inequalities include:

• Read the problem carefully and understand what is being asked.
• Use the correct operations (e.g. adding, subtracting, multiplying, or dividing).
• Check your solution by plugging in a value of x that satisfies the inequality.
• Use a calculator or computer program to check your solution.

Conclusion

Solving inequalities involves isolating the variable on one side of the inequality sign. In this article, we provided a Q&A guide to help you understand and solve inequalities. We discussed how to solve inequalities with fractions and decimals, and provided some tips for solving inequalities. We also discussed some real-world applications of inequalities and provided some examples of inequalities in real-world applications.