Which Of The Following Values Are Solutions To The Inequality $5 \ \textless \ 7 + 5x$?I. 6 II. -5 III. -7 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 make the inequality true. In this article, we will focus on solving the inequality 5 \textless 7+5x5 \ \textless \ 7 + 5x and determine which of the given values are solutions to the inequality.

Understanding the Inequality

The given inequality is 5 \textless 7+5x5 \ \textless \ 7 + 5x. To solve this inequality, we need to isolate the variable xx. The first step is to subtract 7 from both sides of the inequality, which gives us −2 \textless 5x-2 \ \textless \ 5x. Next, we divide both sides of the inequality by 5, which gives us −25 \textless x-\frac{2}{5} \ \textless \ x.

Analyzing the Solutions

Now that we have isolated the variable xx, we can analyze the solutions to the inequality. The inequality −25 \textless x-\frac{2}{5} \ \textless \ x means that xx must be greater than −25-\frac{2}{5}. In other words, xx can take on any value that is greater than −25-\frac{2}{5}.

Evaluating the Given Values

We are given three values: 6, -5, and -7. We need to determine which of these values are solutions to the inequality −25 \textless x-\frac{2}{5} \ \textless \ x. Let's evaluate each value individually.

Value I: 6

To determine if 6 is a solution to the inequality, we need to check if it is greater than −25-\frac{2}{5}. Since 6 is indeed greater than −25-\frac{2}{5}, we can conclude that 6 is a solution to the inequality.

Value II: -5

To determine if -5 is a solution to the inequality, we need to check if it is greater than −25-\frac{2}{5}. Since -5 is not greater than −25-\frac{2}{5}, we can conclude that -5 is not a solution to the inequality.

Value III: -7

To determine if -7 is a solution to the inequality, we need to check if it is greater than −25-\frac{2}{5}. Since -7 is not greater than −25-\frac{2}{5}, we can conclude that -7 is not a solution to the inequality.

Conclusion

In conclusion, the only value that is a solution to the inequality 5 \textless 7+5x5 \ \textless \ 7 + 5x is 6. Therefore, the correct answer is B. I only.

Final Answer

The final answer is B.

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Introduction

In our previous article, we discussed how to solve the inequality 5 \textless 7+5x5 \ \textless \ 7 + 5x and determined which of the given values are solutions to the inequality. In this article, we will provide a Q&A guide to help you better understand how to solve inequalities and answer common questions related to inequalities.

Q&A

Q: What is an inequality?

A: An inequality is a mathematical expression that compares two values using 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 by performing the same operations on both sides of the inequality. This may involve adding, subtracting, multiplying, or dividing 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 \textless bax \ \textless \ b, where aa and bb are constants. A quadratic inequality is an inequality that can be written in the form ax2 \textless bax^2 \ \textless \ b, where aa and bb 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 \textless ax \ \textless \ a, you plot a point to the left of aa. If the inequality is of the form x \textgreater ax \ \textgreater \ a, you plot a point to the right of aa.

Q: What is the solution to the inequality x \textless 5x \ \textless \ 5?

A: The solution to the inequality x \textless 5x \ \textless \ 5 is all real numbers less than 5.

Q: What is the solution to the inequality x \textgreater 5x \ \textgreater \ 5?

A: The solution to the inequality x \textgreater 5x \ \textgreater \ 5 is all real numbers greater than 5.

Q: How do I determine if a value is a solution to an inequality?

A: To determine if a value is a solution to an inequality, you need to substitute the value into the inequality and check if the inequality is true.

Q: What is the difference between a strict inequality and a non-strict inequality?

A: A strict inequality is an inequality that is written with a strict symbol, such as x \textless ax \ \textless \ a or x \textgreater ax \ \textgreater \ a. A non-strict inequality is an inequality that is written with a non-strict symbol, such as x ≤ ax \ \leq \ a or x ≥ ax \ \geq \ a.

Conclusion

In conclusion, solving inequalities involves isolating the variable by performing the same operations on both sides of the inequality. By following the steps outlined in this article, you can solve inequalities and answer common questions related to inequalities.

Final Answer

The final answer is that solving inequalities is a crucial skill in mathematics that can be applied to a wide range of problems. By understanding how to solve inequalities, you can better understand mathematical concepts and solve real-world problems.

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