What Is The Final Step In Solving The Inequality − 2 ( 5 − 4 X ) \textless 6 X − 4 -2(5-4x) \ \textless \ 6x - 4 − 2 ( 5 − 4 X ) \textless 6 X − 4 ?A. X \textless − 3 X \ \textless \ -3 X \textless − 3 B. X \textgreater − 3 X \ \textgreater \ -3 X \textgreater − 3 C. X \textless 3 X \ \textless \ 3 X \textless 3 D. X \textgreater 3 X \ \textgreater \ 3 X \textgreater 3

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Introduction

Solving inequalities is a crucial aspect of mathematics, and it requires a step-by-step approach to arrive at the correct solution. In this article, we will focus on solving the inequality $-2(5-4x) \ \textless \ 6x - 4$ and determine the final step in solving it.

Understanding the Inequality

The given inequality is $-2(5-4x) \ \textless \ 6x - 4$. To solve this inequality, we need to follow the order of operations (PEMDAS) and simplify the expression.

Distributing the Negative 2

The first step is to distribute the negative 2 to the terms inside the parentheses.

$$-2(5-4x) = -10 + 8x$$

So, the inequality becomes:

$$-10 + 8x \ \textless \ 6x - 4$$

Adding 10 to Both Sides

To isolate the variable x, we need to add 10 to both sides of the inequality.

$$-10 + 8x + 10 \ \textless \ 6x - 4 + 10$$

This simplifies to:

$$8x \ \textless \ 6x + 6$$

Subtracting 6x from Both Sides

Next, we need to subtract 6x from both sides of the inequality to get:

$$2x \ \textless \ 6$$

Dividing Both Sides by 2

Finally, we need to divide both sides of the inequality by 2 to solve for x.

$$x \ \textless \ 3$$

Conclusion

The final step in solving the inequality $-2(5-4x) \ \textless \ 6x - 4$ is to divide both sides of the inequality by 2, which gives us $x \ \textless \ 3$. This is the correct solution to the inequality.

Comparison with the Options

Let's compare our solution with the options provided:

A. $x \ \textless \ -3$ B. $x \ \textgreater \ -3$ C. $x \ \textless \ 3$ D. $x \ \textgreater \ 3$

Our solution matches option C, which is $x \ \textless \ 3$.

Final Answer

The final answer is option C, which is $x \ \textless \ 3$.

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Introduction

In our previous article, we solved the inequality $-2(5-4x) \ \textless \ 6x - 4$ and arrived at the final solution of $x \ \textless \ 3$. In this article, we will address some common questions and concerns related to solving this inequality.

Q&A

Q: What is the first step in solving the inequality $-2(5-4x) \ \textless \ 6x - 4$?

A: The first step is to distribute the negative 2 to the terms inside the parentheses. This gives us $-10 + 8x$.

Q: Why do we need to add 10 to both sides of the inequality?

A: We need to add 10 to both sides to isolate the variable x. This helps us to simplify the inequality and make it easier to solve.

Q: What is the purpose of subtracting 6x from both sides of the inequality?

A: Subtracting 6x from both sides helps us to get rid of the x term on the right-hand side of the inequality. This makes it easier to solve for x.

Q: Why do we need to divide both sides of the inequality by 2?

A: We need to divide both sides by 2 to solve for x. This is the final step in solving the inequality.

Q: What is the final solution to the inequality $-2(5-4x) \ \textless \ 6x - 4$?

A: The final solution is $x \ \textless \ 3$.

Q: How do we know which option is correct?

A: We can compare our solution with the options provided. In this case, our solution matches option C, which is $x \ \textless \ 3$.

Q: What if the inequality is not in the simplest form?

A: If the inequality is not in the simplest form, we need to simplify it first. This may involve distributing, combining like terms, or adding/subtracting the same value to both sides.

Q: What if we get stuck while solving the inequality?

A: If we get stuck, we can try to simplify the inequality further or look for alternative solutions. We can also consult with a teacher or tutor for help.

Conclusion

Solving inequalities can be challenging, but with practice and patience, we can master the skills needed to solve them. By following the steps outlined in this article, we can solve the inequality $-2(5-4x) \ \textless \ 6x - 4$ and arrive at the final solution of $x \ \textless \ 3$.

Additional Resources

• For more information on solving inequalities, check out our article on [Solving Linear Inequalities](link to article).
• For practice problems and exercises, try our [Inequality Practice Set](link to practice set).

Final Answer

The final answer is option C, which is $x \ \textless \ 3$.