Solve For $n$ In The Inequality: $-2n - 5 \geq 3$.A. $n \geq -4$ B. $-4 \ \textless \ N$ C. $n \leq -4$ D. $n \ \textless \ -4$
Introduction
In mathematics, inequalities are a fundamental concept that plays a crucial role in solving various problems. A linear inequality is an inequality that involves a linear expression, and it is often represented in the form of ax + b ≥ c or ax + b ≤ c, where a, b, and c are constants. In this article, we will focus on solving linear inequalities, specifically the inequality -2n - 5 ≥ 3.
Understanding the Inequality
The given inequality is -2n - 5 ≥ 3. To solve this inequality, we need to isolate the variable n. The first step is to add 5 to both sides of the inequality, which gives us -2n ≥ 8.
Isolating the Variable
Next, we need to isolate the variable n. To do this, we divide both sides of the inequality by -2. However, when we divide or multiply an inequality by a negative number, we need to reverse the direction of the inequality sign. Therefore, the inequality becomes n ≤ -4.
Analyzing the Solution
Now that we have solved the inequality, let's analyze the solution. The solution n ≤ -4 indicates that the value of n is less than or equal to -4. This means that any value of n that is less than or equal to -4 satisfies the inequality.
Comparing the Solution with the Options
Let's compare the solution n ≤ -4 with the given options:
- A. n ≥ -4: This option is incorrect because the solution is n ≤ -4, not n ≥ -4.
- B. -4 < n: This option is incorrect because the solution is n ≤ -4, not -4 < n.
- C. n ≤ -4: This option is correct because it matches the solution we obtained.
- D. n < -4: This option is incorrect because the solution is n ≤ -4, not n < -4.
Conclusion
In conclusion, the solution to the inequality -2n - 5 ≥ 3 is n ≤ -4. This means that any value of n that is less than or equal to -4 satisfies the inequality. We compared the solution with the given options and found that option C is the correct answer.
Tips and Tricks
When solving linear inequalities, remember to:
- Add or subtract the same value to both sides of the inequality.
- Multiply or divide both sides of the inequality by the same value.
- Reverse the direction of the inequality sign when dividing or multiplying by a negative number.
- Analyze the solution and compare it with the given options.
Practice Problems
Try solving the following linear inequalities:
- 3x + 2 ≥ 5
- 2x - 3 ≤ 1
- x/2 ≥ 3
- 4x - 2 ≤ 6
Introduction
In mathematics, inequalities are a fundamental concept that plays a crucial role in solving various problems. A linear inequality is an inequality that involves a linear expression, and it is often represented in the form of ax + b ≥ c or ax + b ≤ c, where a, b, and c are constants. In this article, we will focus on solving linear inequalities, specifically the inequality -2n - 5 ≥ 3.
Understanding the Inequality
The given inequality is -2n - 5 ≥ 3. To solve this inequality, we need to isolate the variable n. The first step is to add 5 to both sides of the inequality, which gives us -2n ≥ 8.
Isolating the Variable
Next, we need to isolate the variable n. To do this, we divide both sides of the inequality by -2. However, when we divide or multiply an inequality by a negative number, we need to reverse the direction of the inequality sign. Therefore, the inequality becomes n ≤ -4.
Analyzing the Solution
Now that we have solved the inequality, let's analyze the solution. The solution n ≤ -4 indicates that the value of n is less than or equal to -4. This means that any value of n that is less than or equal to -4 satisfies the inequality.
Comparing the Solution with the Options
Let's compare the solution n ≤ -4 with the given options:
- A. n ≥ -4: This option is incorrect because the solution is n ≤ -4, not n ≥ -4.
- B. -4 < n: This option is incorrect because the solution is n ≤ -4, not -4 < n.
- C. n ≤ -4: This option is correct because it matches the solution we obtained.
- D. n < -4: This option is incorrect because the solution is n ≤ -4, not n < -4.
Conclusion
In conclusion, the solution to the inequality -2n - 5 ≥ 3 is n ≤ -4. This means that any value of n that is less than or equal to -4 satisfies the inequality. We compared the solution with the given options and found that option C is the correct answer.
Tips and Tricks
When solving linear inequalities, remember to:
- Add or subtract the same value to both sides of the inequality.
- Multiply or divide both sides of the inequality by the same value.
- Reverse the direction of the inequality sign when dividing or multiplying by a negative number.
- Analyze the solution and compare it with the given options.
Practice Problems
Try solving the following linear inequalities:
- 3x + 2 ≥ 5
- 2x - 3 ≤ 1
- x/2 ≥ 3
- 4x - 2 ≤ 6
Solving Linear Inequalities: A Step-by-Step Guide =====================================================
Q&A: Solving Linear Inequalities
Q: What is a linear inequality?
A: A linear inequality is an inequality that involves a linear expression, and it is often represented in the form of ax + b ≥ c or ax + b ≤ c, where a, b, and c are constants.
Q: How do I solve a linear inequality?
A: To solve a linear inequality, you need to isolate the variable. 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 value. However, when you divide or multiply an inequality by a negative number, you need to reverse the direction of the inequality sign.
Q: What is the difference between a linear inequality and a linear equation?
A: A linear equation is an equation that involves a linear expression, and it is often represented in the form of ax + b = c, where a, b, and c are constants. A linear inequality, on the other hand, is an inequality that involves a linear expression, and it is often represented in the form of ax + b ≥ c or ax + b ≤ c.
Q: How do I know which direction to reverse the inequality sign when dividing or multiplying by a negative number?
A: When dividing or multiplying an inequality by a negative number, you need to reverse the direction of the inequality sign. For example, if you have the inequality 2x ≥ 3 and you divide both sides by -2, the inequality becomes x ≤ -3/2.
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 2x + 3 ≥ 5, you can subtract 3 from both sides to get 2x ≥ 2.
Q: Can I multiply or divide both sides of an inequality by the same value?
A: Yes, you can multiply or divide both sides of an inequality by the same value. However, when you divide or multiply an inequality by a negative number, you need to reverse the direction of the inequality sign.
Q: How do I analyze the solution to a linear inequality?
A: To analyze the solution to a linear inequality, you need to determine the values of the variable that satisfy the inequality. You can do this by comparing the solution to the given options.
Q: What are some common mistakes to avoid when solving linear inequalities?
A: Some common mistakes to avoid when solving linear inequalities include:
- Not reversing the direction of the inequality sign when dividing or multiplying by a negative number.
- Not adding or subtracting the same value to both sides of the inequality.
- Not multiplying or dividing both sides of the inequality by the same value.
- Not analyzing the solution and comparing it to the given options.
Q: How do I practice solving linear inequalities?
A: You can practice solving linear inequalities by trying out different problems and checking your solutions. You can also use online resources or math textbooks to find practice problems and solutions.
Conclusion
In conclusion, solving linear inequalities requires a step-by-step approach. You need to isolate the variable, analyze the solution, and compare it to the given options. By following these steps and avoiding common mistakes, you can become proficient in solving linear inequalities.
Tips and Tricks
- Always add or subtract the same value to both sides of the inequality.
- Always multiply or divide both sides of the inequality by the same value.
- Always reverse the direction of the inequality sign when dividing or multiplying by a negative number.
- Always analyze the solution and compare it to the given options.
Practice Problems
Try solving the following linear inequalities:
- 3x + 2 ≥ 5
- 2x - 3 ≤ 1
- x/2 ≥ 3
- 4x - 2 ≤ 6
Introduction
In mathematics, inequalities are a fundamental concept that plays a crucial role in solving various problems. A linear inequality is an inequality that involves a linear expression, and it is often represented in the form of ax + b ≥ c or ax + b ≤ c, where a, b, and c are constants. In this article, we will focus on solving linear inequalities, specifically the inequality -2n - 5 ≥ 3.
Understanding the Inequality
The given inequality is -2n - 5 ≥ 3. To solve this inequality, we need to isolate the variable n. The first step is to add 5 to both sides of the inequality, which gives us -2n ≥ 8.
Isolating the Variable
Next, we need to isolate the variable n. To do this, we divide both sides of the inequality by -2. However, when we divide or multiply an inequality by a negative number, we need to reverse the direction of the inequality sign. Therefore, the inequality becomes n ≤ -4.
Analyzing the Solution
Now that we have solved the inequality, let's analyze the solution. The solution n ≤ -4 indicates that the value of n is less than or equal to -4. This means that any value of n that is less than or equal to -4 satisfies the inequality.
Comparing the Solution with the Options
Let's compare the solution n ≤ -4 with the given options:
- A. n ≥ -4: This option is incorrect because the solution is n ≤ -4, not n ≥ -4.
- B. -4 < n: This option is incorrect because the solution is n ≤ -4, not -4 < n.
- C. n ≤ -4: This option is correct because it matches the solution we obtained.
- D. n < -4: This option is incorrect because the solution is n ≤ -4, not n < -4.
Conclusion
In conclusion, the solution to the inequality -2n - 5 ≥ 3 is n ≤ -4. This means that any value of n that is less than or equal to -4 satisfies the inequality. We compared the solution with the given options and found that option C is the correct answer.
Tips and Tricks
When solving linear inequalities, remember to:
- Add or subtract the same value to both sides of the inequality.
- Multiply or divide both sides of the inequality by the same value.
- Reverse the direction of the inequality sign when dividing or multiplying by a negative number.
- Analyze the solution and compare it with the given options.
Practice Problems
Try solving the following linear inequalities:
- 3x + 2 ≥ 5
- 2x - 3 ≤ 1
- x/2 ≥ 3
- 4x - 2 ≤ 6