Solve The Inequality:$7x - 8 \ \textgreater \ 34$Choose The Correct Solution:A. $x \ \textgreater \ 3 \frac{5}{7}$B. $x \ \textless \ 3 \frac{5}{7}$C. $x \ \textless \ 6$D. $x \ \textgreater \ 6$

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Introduction

In this article, we will focus on solving the given inequality $7x - 8 \ \textgreater \ 34$. We will use algebraic methods to isolate the variable $x$ and determine the correct solution. The inequality is a linear inequality, and we will use the properties of linear inequalities to solve it.

Understanding the Inequality

The given inequality is $7x - 8 \ \textgreater \ 34$. This means that the expression $7x - 8$ is greater than $34$. To solve this inequality, we need to isolate the variable $x$.

Adding 8 to Both Sides

To isolate the variable $x$, we can add $8$ to both sides of the inequality. This will give us:

$$7x - 8 + 8 \ \textgreater \ 34 + 8$$

Simplifying the left-hand side, we get:

$$7x \ \textgreater \ 42$$

Dividing Both Sides by 7

To isolate the variable $x$, we can divide both sides of the inequality by $7$. This will give us:

$$\frac{7x}{7} \ \textgreater \ \frac{42}{7}$$

Simplifying the left-hand side, we get:

$$x \ \textgreater \ 6$$

Conclusion

Therefore, the correct solution to the inequality $7x - 8 \ \textgreater \ 34$ is $x \ \textgreater \ 6$. This means that the value of $x$ must be greater than $6$.

Comparison with Other Options

Let's compare our solution with the other options:

• Option A: $x \ \textgreater \ 3 \frac{5}{7}$
• Option B: $x \ \textless \ 3 \frac{5}{7}$
• Option C: $x \ \textless \ 6$
• Option D: $x \ \textgreater \ 6$

Our solution is $x \ \textgreater \ 6$, which is option D. Therefore, the correct answer is option D.

Final Answer

The final answer is option D: $x \ \textgreater \ 6$.

Frequently Asked Questions

• Q: What is the correct solution to the inequality $7x - 8 \ \textgreater \ 34$? A: The correct solution is $x \ \textgreater \ 6$.
• Q: How do I solve a linear inequality? A: To solve a linear inequality, you can add or subtract the same value from both sides, and then divide both sides by the same non-zero value.
• 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 $ax + b \ \textgreater \ c$, where $a$, $b$, and $c$ are constants. A quadratic inequality is an inequality that can be written in the form $ax^2 + bx + c \ \textgreater \ d$, where $a$, $b$, $c$, and $d$ are constants.

Conclusion

In this article, we solved the inequality $7x - 8 \ \textgreater \ 34$ using algebraic methods. We added $8$ to both sides of the inequality, and then divided both sides by $7$ to isolate the variable $x$. The correct solution is $x \ \textgreater \ 6$. We also compared our solution with the other options and found that the correct answer is option D.

Introduction

In our previous article, we solved the inequality $7x - 8 \ \textgreater \ 34$ using algebraic methods. In this article, we will provide a Q&A guide to help you understand how to solve inequalities. We will cover common questions and topics related to solving inequalities, including linear inequalities and quadratic inequalities.

Q&A Guide

Q: What is a linear inequality?

A: A linear inequality is an inequality that can be written in the form $ax + b \ \textgreater \ c$, where $a$, $b$, and $c$ are constants. For example, $2x + 3 \ \textgreater \ 5$ is a linear inequality.

Q: How do I solve a linear inequality?

A: To solve a linear inequality, you can add or subtract the same value from both sides, and then divide both sides by the same non-zero value. For example, to solve the inequality $2x + 3 \ \textgreater \ 5$, you can subtract $3$ from both sides to get $2x \ \textgreater \ 2$, and then divide both sides by $2$ to get $x \ \textgreater \ 1$.

Q: What is a quadratic inequality?

A: A quadratic inequality is an inequality that can be written in the form $ax^2 + bx + c \ \textgreater \ d$, where $a$, $b$, $c$, and $d$ are constants. For example, $x^2 + 4x + 4 \ \textgreater \ 0$ is a quadratic inequality.

Q: How do I solve a quadratic inequality?

A: To solve a quadratic inequality, you can factor the quadratic expression, and then use the sign of the expression to determine the solution. For example, to solve the inequality $x^2 + 4x + 4 \ \textgreater \ 0$, you can factor the expression as $(x + 2)^2 \ \textgreater \ 0$, and then use the sign of the expression to determine that the solution is $x \ \textless \ -2$ or $x \ \textgreater \ -2$.

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 $ax + b \ \textgreater \ c$, where $a$, $b$, and $c$ are constants. A quadratic inequality is an inequality that can be written in the form $ax^2 + bx + c \ \textgreater \ d$, where $a$, $b$, $c$, and $d$ are constants.

Q: How do I determine the solution to a linear inequality?

A: To determine the solution to a linear inequality, you can use the following steps:

1. Add or subtract the same value from both sides of the inequality.
2. Divide both sides of the inequality by the same non-zero value.
3. Use the sign of the expression to determine the solution.

Q: How do I determine the solution to a quadratic inequality?

A: To determine the solution to a quadratic inequality, you can use the following steps:

1. Factor the quadratic expression.
2. Use the sign of the expression to determine the solution.
3. Use the zeros of the quadratic expression to determine the solution.

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 using the correct signs when adding or subtracting values.
• Not dividing both sides of the inequality by the same non-zero value.
• Not using the correct method to determine the solution.

Conclusion

In this article, we provided a Q&A guide to help you understand how to solve inequalities. We covered common questions and topics related to solving linear inequalities and quadratic inequalities. We also provided tips and tricks to help you avoid common mistakes when solving inequalities.

Frequently Asked Questions

• Q: What is a linear inequality? A: A linear inequality is an inequality that can be written in the form $ax + b \ \textgreater \ c$, where $a$, $b$, and $c$ are constants.
• Q: How do I solve a linear inequality? A: To solve a linear inequality, you can add or subtract the same value from both sides, and then divide both sides by the same non-zero value.
• Q: What is a quadratic inequality? A: A quadratic inequality is an inequality that can be written in the form $ax^2 + bx + c \ \textgreater \ d$, where $a$, $b$, $c$, and $d$ are constants.
• Q: How do I solve a quadratic inequality? A: To solve a quadratic inequality, you can factor the quadratic expression, and then use the sign of the expression to determine the solution.

Final Answer

The final answer is that solving inequalities requires a clear understanding of the concepts and methods involved. By following the steps outlined in this article, you can develop the skills and knowledge needed to solve inequalities with confidence.