Solve The Inequality D − 6.63 ≥ 13 \frac{d}{-6.63} \geq 13 − 6.63 D ​ ≥ 13 .

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Introduction

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In this article, we will delve into the world of inequalities and learn how to solve them. Specifically, we will focus on solving the inequality $\frac{d}{-6.63} \geq 13$. This type of problem is commonly encountered in algebra and is an essential skill to master for anyone looking to excel in mathematics.

Understanding the Problem

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Before we dive into the solution, let's break down the problem and understand what it's asking for. The inequality $\frac{d}{-6.63} \geq 13$ is a comparison between two values. We are given a fraction $\frac{d}{-6.63}$ and we need to find the value of $d$ that satisfies the condition $\frac{d}{-6.63} \geq 13$. In other words, we need to find the minimum value of $d$ that makes the fraction greater than or equal to 13.

Step 1: Multiply Both Sides by -6.63

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To solve the inequality, we need to isolate the variable $d$. The first step is to multiply both sides of the inequality by -6.63. This will eliminate the fraction and give us an inequality in terms of $d$.

$\frac{d}{-6.63} \geq 13$

Multiplying both sides by -6.63 gives us:

$d \leq -13 \times -6.63$

Step 2: Simplify the Right-Hand Side

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Now that we have multiplied both sides by -6.63, we need to simplify the right-hand side of the inequality. We can do this by multiplying -13 by -6.63.

$d \leq 86.19$

Step 3: Write the Final Answer

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Now that we have simplified the right-hand side, we can write the final answer. The inequality $\frac{d}{-6.63} \geq 13$ is equivalent to the inequality $d \leq 86.19$. Therefore, the final answer is:

$d \leq 86.19$

Conclusion

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Solving the inequality $\frac{d}{-6.63} \geq 13$ requires us to isolate the variable $d$ and simplify the right-hand side of the inequality. By following the steps outlined above, we can find the minimum value of $d$ that satisfies the condition. In this case, the final answer is $d \leq 86.19$.

Frequently Asked Questions

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Q: What is the purpose of multiplying both sides of the inequality by -6.63?

A: The purpose of multiplying both sides of the inequality by -6.63 is to eliminate the fraction and give us an inequality in terms of $d$.

Q: How do we simplify the right-hand side of the inequality?

A: We can simplify the right-hand side of the inequality by multiplying -13 by -6.63.

Q: What is the final answer to the inequality $\frac{d}{-6.63} \geq 13$?

A: The final answer to the inequality $\frac{d}{-6.63} \geq 13$ is $d \leq 86.19$.

Example Problems

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Problem 1: Solve the inequality $\frac{x}{-2.5} \geq 10$

To solve this inequality, we need to multiply both sides by -2.5 and simplify the right-hand side.

$\frac{x}{-2.5} \geq 10$

Multiplying both sides by -2.5 gives us:

$x \leq -10 \times -2.5$

Simplifying the right-hand side gives us:

$x \leq 25$

Problem 2: Solve the inequality $\frac{y}{-3.2} \geq 8$

To solve this inequality, we need to multiply both sides by -3.2 and simplify the right-hand side.

$\frac{y}{-3.2} \geq 8$

Multiplying both sides by -3.2 gives us:

$y \leq -8 \times -3.2$

Simplifying the right-hand side gives us:

$y \leq 25.6$

Tips and Tricks

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Tip 1: Always multiply both sides of the inequality by the same value

When solving an inequality, it's essential to multiply both sides by the same value. This will ensure that the inequality remains true.

Tip 2: Simplify the right-hand side of the inequality

Simplifying the right-hand side of the inequality will make it easier to read and understand.

Tip 3: Check your work

After solving the inequality, it's essential to check your work to ensure that the solution is correct.

Conclusion

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Solving the inequality $\frac{d}{-6.63} \geq 13$ requires us to isolate the variable $d$ and simplify the right-hand side of the inequality. By following the steps outlined above, we can find the minimum value of $d$ that satisfies the condition. In this case, the final answer is $d \leq 86.19$.

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Introduction

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Solving inequalities can be a challenging task, but with the right guidance, it can become a breeze. In this article, we will answer some of the most frequently asked questions about solving inequalities. Whether you're a student struggling with algebra or a teacher looking for ways to explain complex concepts, this article is for you.

Q&A

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Q: What is an inequality?

A: An inequality is a mathematical statement that compares two values using a comparison operator 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. This can be done 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 statement that states that two values are equal. An inequality, on the other hand, states that two values are not equal, but one value is greater than, less than, greater than or equal to, or less than or equal to the other value.

Q: How do I know which direction to multiply or divide both sides of the inequality?

A: When multiplying or dividing both sides of an inequality, you need to multiply or divide both sides by the same value. If you multiply or divide both sides by a negative value, you need to reverse the direction of the inequality sign.

Q: What is the order of operations when solving an inequality?

A: When solving an inequality, you need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate any expressions inside parentheses.
2. Exponents: Evaluate any exponential expressions.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Q: How do I check my work when solving an inequality?

A: To check your work, you need to plug your solution back into the original inequality and verify that it is true. If the solution is not true, you need to re-evaluate your work and try again.

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 multiplying or dividing both sides of the inequality by the same value
• Not reversing the direction of the inequality sign when multiplying or dividing both sides by a negative value
• Not checking your work

Example Problems

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Problem 1: Solve the inequality $2x + 5 \geq 11$

To solve this inequality, we need to isolate the variable $x$.

$2x + 5 \geq 11$

Subtracting 5 from both sides gives us:

$2x \geq 6$

Dividing both sides by 2 gives us:

$x \geq 3$

Problem 2: Solve the inequality $x - 3 \leq 7$

To solve this inequality, we need to isolate the variable $x$.

$x - 3 \leq 7$

Adding 3 to both sides gives us:

$x \leq 10$

Tips and Tricks

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Tip 1: Always follow the order of operations

When solving an inequality, it's essential to follow the order of operations (PEMDAS) to ensure that you get the correct solution.

Tip 2: Check your work

After solving an inequality, it's essential to check your work to ensure that the solution is correct.

Tip 3: Use a calculator to check your work

If you're unsure about your solution, you can use a calculator to check your work.

Conclusion

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Solving inequalities can be a challenging task, but with the right guidance, it can become a breeze. By following the steps outlined in this article, you can solve inequalities with confidence. Remember to always follow the order of operations, check your work, and use a calculator to check your work if needed. With practice and patience, you'll become a pro at solving inequalities in no time!