What Is The Solution Set To The Inequality $-3x + 5.9 \geq -15.4$ For $x$ In The Set $\{-10, -5, 0, 5, 10\}$?

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Introduction

In this article, we will explore the solution set to the inequality $-3x + 5.9 \geq -15.4$ for $x$ in the set $\{-10, -5, 0, 5, 10\}$. This involves solving the inequality and then finding the values of $x$ that satisfy the inequality from the given set.

Understanding the Inequality

The given inequality is $-3x + 5.9 \geq -15.4$. To solve this inequality, we need to isolate the variable $x$. We can start by subtracting $5.9$ from both sides of the inequality.

-3x + 5.9 - 5.9 \geq -15.4 - 5.9

This simplifies to:

-3x \geq -21.3

Solving the Inequality

To solve the inequality, we need to isolate the variable $x$. We can do this by dividing both sides of the inequality by $-3$. However, when we divide or multiply an inequality by a negative number, we need to reverse the direction of the inequality.

\frac{-3x}{-3} \leq \frac{-21.3}{-3}

This simplifies to:

x \leq 7.1

Finding the Solution Set

Now that we have solved the inequality, we need to find the values of $x$ that satisfy the inequality from the given set $\{-10, -5, 0, 5, 10\}$. We can do this by substituting each value of $x$ into the inequality and checking if it is true.

Substituting $x = -10$

-3(-10) + 5.9 \geq -15.4
30 + 5.9 \geq -15.4
35.9 \geq -15.4

This is true, so $x = -10$ is a solution.

Substituting $x = -5$

-3(-5) + 5.9 \geq -15.4
15 + 5.9 \geq -15.4
20.9 \geq -15.4

This is true, so $x = -5$ is a solution.

Substituting $x = 0$

-3(0) + 5.9 \geq -15.4
0 + 5.9 \geq -15.4
5.9 \geq -15.4

This is true, so $x = 0$ is a solution.

Substituting $x = 5$

-3(5) + 5.9 \geq -15.4
-15 + 5.9 \geq -15.4
-9.1 \geq -15.4

This is false, so $x = 5$ is not a solution.

Substituting $x = 10$

-3(10) + 5.9 \geq -15.4
-30 + 5.9 \geq -15.4
-24.1 \geq -15.4

This is false, so $x = 10$ is not a solution.

Conclusion

In conclusion, the solution set to the inequality $-3x + 5.9 \geq -15.4$ for $x$ in the set $\{-10, -5, 0, 5, 10\}$ is $\{-10, -5, 0\}$. These are the values of $x$ that satisfy the inequality from the given set.

Final Answer

The final answer is $\boxed{\{-10, -5, 0\}}$.

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Introduction

In our previous article, we explored the solution set to the inequality $-3x + 5.9 \geq -15.4$ for $x$ in the set $\{-10, -5, 0, 5, 10\}$. We found that the solution set is $\{-10, -5, 0\}$. In this article, we will answer some frequently asked questions about solving the inequality.

Q&A

Q: What is the first step in solving the inequality $-3x + 5.9 \geq -15.4$?

A: The first step in solving the inequality is to isolate the variable $x$. We can do this by subtracting $5.9$ from both sides of the inequality.

Q: Why do we need to reverse the direction of the inequality when we divide or multiply by a negative number?

A: When we divide or multiply an inequality by a negative number, we need to reverse the direction of the inequality. This is because multiplying or dividing by a negative number changes the sign of the inequality.

Q: How do we find the solution set to the inequality?

A: To find the solution set, we need to substitute each value of $x$ into the inequality and check if it is true. We can do this by plugging in each value of $x$ into the inequality and checking if it satisfies the inequality.

Q: What is the solution set to the inequality $-3x + 5.9 \geq -15.4$ for $x$ in the set $\{-10, -5, 0, 5, 10\}$?

A: The solution set to the inequality $-3x + 5.9 \geq -15.4$ for $x$ in the set $\{-10, -5, 0, 5, 10\}$ is $\{-10, -5, 0\}$.

Q: How do we know if a value of $x$ is a solution to the inequality?

A: We can check if a value of $x$ is a solution to the inequality by plugging it into the inequality and checking if it satisfies the inequality. If the inequality is true, then the value of $x$ is a solution.

Q: What is the final answer to the inequality $-3x + 5.9 \geq -15.4$?

A: The final answer to the inequality $-3x + 5.9 \geq -15.4$ is $\boxed{\{-10, -5, 0\}}$.

Conclusion

In conclusion, solving the inequality $-3x + 5.9 \geq -15.4$ involves isolating the variable $x$, reversing the direction of the inequality when dividing or multiplying by a negative number, and finding the solution set by substituting each value of $x$ into the inequality. We hope this Q&A article has been helpful in answering your questions about solving the inequality.

Final Answer

The final answer is $\boxed{\{-10, -5, 0\}}$.