Which Of The Following Values Are Solutions To The Inequality − 3 ≤ X − 4 -3 \leq X-4 − 3 ≤ X − 4 ?I. 1 II. -3 III. -5 Answer Options: A. None B. I Only C. II Only D. III Only E. I And II F. I And III G. II And III H. I, II, And III

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Introduction

Inequalities are mathematical expressions that compare two values using greater than, less than, greater than or equal to, or less than or equal to. Solving inequalities involves finding the values of the variable that satisfy the given inequality. In this article, we will focus on solving the inequality −3≤x−4-3 \leq x-4 and determine which of the given values are solutions to the inequality.

Understanding the Inequality

The given inequality is −3≤x−4-3 \leq x-4. To solve this inequality, we need to isolate the variable xx. We can start by adding 4 to both sides of the inequality, which gives us −3+4≤x−4+4-3 + 4 \leq x - 4 + 4. This simplifies to 1≤x1 \leq x.

Isolating the Variable

Now that we have isolated the variable xx, we can see that the inequality is in the form 1≤x1 \leq x. This means that xx must be greater than or equal to 1.

Analyzing the Answer Options

Now that we have solved the inequality, we can analyze the answer options to determine which values are solutions to the inequality.

Option I: 1

Since the inequality is 1≤x1 \leq x, we can see that xx must be greater than or equal to 1. Therefore, option I, which is 1, is a solution to the inequality.

Option II: -3

Since the inequality is 1≤x1 \leq x, we can see that xx must be greater than or equal to 1. Therefore, option II, which is -3, is not a solution to the inequality.

Option III: -5

Since the inequality is 1≤x1 \leq x, we can see that xx must be greater than or equal to 1. Therefore, option III, which is -5, is not a solution to the inequality.

Conclusion

Based on our analysis, we can see that only option I, which is 1, is a solution to the inequality −3≤x−4-3 \leq x-4. Therefore, the correct answer is B. I only.

Frequently Asked Questions

Q: What is the solution to the inequality −3≤x−4-3 \leq x-4?

A: The solution to the inequality −3≤x−4-3 \leq x-4 is x≥1x \geq 1.

Q: Which of the given values are solutions to the inequality −3≤x−4-3 \leq x-4?

A: Only option I, which is 1, is a solution to the inequality −3≤x−4-3 \leq x-4.

Q: How do I solve an inequality?

A: To solve an inequality, you need to isolate the variable by performing the same operations on both sides of the inequality.

Final Answer

The final answer is B. I only.

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Introduction

Inequalities are mathematical expressions that compare two values using greater than, less than, greater than or equal to, or less than or equal to. Solving inequalities involves finding the values of the variable that satisfy the given inequality. In this article, we will focus on solving the inequality −3≤x−4-3 \leq x-4 and determine which of the given values are solutions to the inequality.

Understanding the Inequality

The given inequality is −3≤x−4-3 \leq x-4. To solve this inequality, we need to isolate the variable xx. We can start by adding 4 to both sides of the inequality, which gives us −3+4≤x−4+4-3 + 4 \leq x - 4 + 4. This simplifies to 1≤x1 \leq x.

Isolating the Variable

Now that we have isolated the variable xx, we can see that the inequality is in the form 1≤x1 \leq x. This means that xx must be greater than or equal to 1.

Analyzing the Answer Options

Now that we have solved the inequality, we can analyze the answer options to determine which values are solutions to the inequality.

Option I: 1

Since the inequality is 1≤x1 \leq x, we can see that xx must be greater than or equal to 1. Therefore, option I, which is 1, is a solution to the inequality.

Option II: -3

Since the inequality is 1≤x1 \leq x, we can see that xx must be greater than or equal to 1. Therefore, option II, which is -3, is not a solution to the inequality.

Option III: -5

Since the inequality is 1≤x1 \leq x, we can see that xx must be greater than or equal to 1. Therefore, option III, which is -5, is not a solution to the inequality.

Conclusion

Based on our analysis, we can see that only option I, which is 1, is a solution to the inequality −3≤x−4-3 \leq x-4. Therefore, the correct answer is B. I only.

Frequently Asked Questions

Q: What is the solution to the inequality −3≤x−4-3 \leq x-4?

A: The solution to the inequality −3≤x−4-3 \leq x-4 is x≥1x \geq 1.

Q: Which of the given values are solutions to the inequality −3≤x−4-3 \leq x-4?

A: Only option I, which is 1, is a solution to the inequality −3≤x−4-3 \leq x-4.

Q: How do I solve an inequality?

A: To solve an inequality, you need to isolate the variable by performing the same operations on both sides of the inequality.

Q: What is the difference between a linear inequality and a quadratic inequality?

A: A linear inequality is an inequality that can be written in the form ax+b≤cax + b \leq c, where aa, bb, and cc are constants. A quadratic inequality is an inequality that can be written in the form ax2+bx+c≤0ax^2 + bx + c \leq 0, where aa, bb, and cc are constants.

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 to the inequality. If the inequality is of the form x≥ax \geq a, you need to plot a closed circle at the point aa. If the inequality is of the form x>ax > a, you need to plot an open circle at the point aa.

Q: What is the relationship between inequalities and equations?

A: Inequalities and equations are related in that they both involve solving for a variable. However, the main difference between the two is that inequalities involve a comparison between two values, while equations involve an equality between two values.

Tips and Tricks

Tip 1: Always isolate the variable

When solving an inequality, it's essential to isolate the variable by performing the same operations on both sides of the inequality.

Tip 2: Use the correct symbols

When graphing an inequality on a number line, it's essential to use the correct symbols. A closed circle represents a solution to the inequality, while an open circle represents a non-solution.

Tip 3: Check your work

When solving an inequality, it's essential to check your work by plugging in values that satisfy the inequality to ensure that the solution is correct.

Conclusion

Solving inequalities involves finding the values of the variable that satisfy the given inequality. By following the steps outlined in this article, you can solve inequalities and determine which values are solutions to the inequality. Remember to always isolate the variable, use the correct symbols, and check your work to ensure that the solution is correct.

Final Answer

The final answer is B. I only.