What Is The Solution To $-2(8x - 4) \ \textless \ 2x + 5$?A. $x \ \textgreater \ \frac{1}{6}$ B. $x \ \textless \ \frac{1}{6}$ C. $x \ \textgreater \ 6$ D. $x \ \textless \ 6$

Introduction

In this article, we will explore the solution to the given inequality $-2(8x - 4) \ \textless \ 2x + 5$. This involves simplifying the inequality, isolating the variable, and determining the range of values for which the inequality holds true. We will use algebraic manipulations and mathematical properties to solve the inequality and provide the correct solution.

Step 1: Simplify the Inequality

The first step in solving the inequality is to simplify the left-hand side by distributing the negative 2 to the terms inside the parentheses.

$$-2(8x - 4) \ \textless \ 2x + 5$$

$$-16x + 8 \ \textless \ 2x + 5$$

Step 2: Isolate the Variable

Next, we need to isolate the variable x by moving all the terms containing x to one side of the inequality and the constant terms to the other side.

$$-16x + 8 \ \textless \ 2x + 5$$

$$-16x - 2x \ \textless \ 5 - 8$$

$$-18x \ \textless \ -3$$

Step 3: Divide by the Coefficient

To solve for x, we need to divide both sides of the inequality by the coefficient of x, which is -18.

$$-18x \ \textless \ -3$$

$$\frac{-18x}{-18} \ \textless \ \frac{-3}{-18}$$

$$x \ \textgreater \ \frac{1}{6}$$

Conclusion

The solution to the inequality $-2(8x - 4) \ \textless \ 2x + 5$ is $x \ \textgreater \ \frac{1}{6}$. This means that the value of x must be greater than $\frac{1}{6}$ for the inequality to hold true.

Final Answer

The final answer is: $\boxed{A}$

Introduction

In this article, we will address some of the most frequently asked questions about the inequality $-2(8x - 4) \ \textless \ 2x + 5$. We will provide detailed explanations and examples to help clarify any doubts and provide a deeper understanding of the topic.

Q: What is the first step in solving the inequality?

A: The first step in solving the inequality is to simplify the left-hand side by distributing the negative 2 to the terms inside the parentheses.

Q: How do I isolate the variable x?

A: To isolate the variable x, you need to move all the terms containing x to one side of the inequality and the constant terms to the other side. This involves adding or subtracting the same value to both sides of the inequality.

Q: What is the next step after isolating the variable x?

A: After isolating the variable x, the next step is to divide both sides of the inequality by the coefficient of x. This will give you the final solution to the inequality.

Q: What is the solution to the inequality?

A: The solution to the inequality $-2(8x - 4) \ \textless \ 2x + 5$ is $x \ \textgreater \ \frac{1}{6}$. This means that the value of x must be greater than $\frac{1}{6}$ for the inequality to hold true.

Q: What if the inequality is in the form of $x \ \textless \ a$ or $x \ \textgreater \ a$?

A: If the inequality is in the form of $x \ \textless \ a$ or $x \ \textgreater \ a$, you can simply replace the inequality sign with the corresponding sign. For example, if the inequality is $x \ \textless \ a$, you can replace it with $x \ \textless \ \frac{1}{6}$.

Q: Can I use a calculator to solve the inequality?

A: Yes, you can use a calculator to solve the inequality. However, it's always a good idea to check your work by plugging in some values to make sure the inequality holds true.

Q: What if I get a different solution using a calculator?

A: If you get a different solution using a calculator, it's possible that there's an error in your calculation. Double-check your work and make sure you're using the correct values.

Q: Can I use the same method to solve other inequalities?

A: Yes, you can use the same method to solve other inequalities. The steps involved in solving an inequality are the same, regardless of the specific inequality.

Conclusion

In this article, we have addressed some of the most frequently asked questions about the inequality $-2(8x - 4) \ \textless \ 2x + 5$. We have provided detailed explanations and examples to help clarify any doubts and provide a deeper understanding of the topic.

Final Answer

The final answer is: $\boxed{A}$