Select The Values That Make The Inequality − X ≥ − 7 -x \geq -7 − X ≥ − 7 True. Then Write An Equivalent Inequality In Terms Of X X X .(Numbers Written In Order From Least To Greatest Going Across.)Answer Attempt 1 Out Of 2:-12, -8, -7.1, -7, -6.9, -6,

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 $-x \geq -7$ and writing an equivalent inequality in terms of $x$.

Understanding the Inequality

The given inequality is $-x \geq -7$. To solve this inequality, we need to isolate the variable $x$. The inequality states that the value of $-x$ is greater than or equal to $-7$. This means that the value of $x$ is less than or equal to $7$.

Step 1: Multiply Both Sides by -1

To isolate the variable $x$, we need to get rid of the negative sign in front of the $x$. We can do this by multiplying both sides of the inequality by $-1$. However, when we multiply or divide both sides of an inequality by a negative number, we need to reverse the direction of the inequality sign.

-x ≥ -7

Multiplying both sides by $-1$ gives us:

x ≤ 7

Step 2: Write an Equivalent Inequality in Terms of $x$

Now that we have isolated the variable $x$, we can write an equivalent inequality in terms of $x$. The equivalent inequality is $x \leq 7$.

Finding the Values that Make the Inequality True

To find the values that make the inequality $x \leq 7$ true, we need to consider all the values of $x$ that are less than or equal to $7$. This includes all the integers and fractions between $-∞$ and $7$.

Selecting the Correct Values

The problem asks us to select the values that make the inequality $-x \geq -7$ true. Based on our solution, we know that the inequality is equivalent to $x \leq 7$. Therefore, the values that make the inequality true are all the values of $x$ that are less than or equal to $7$.

Answer

The correct answer is:

• -12
• -8
• -7.1
• -7
• -6.9
• -6

These values are all less than or equal to $7$, which makes the inequality $-x \geq -7$ true.

Conclusion

Solving inequalities involves finding the values of the variable that make the inequality true. In this article, we solved the inequality $-x \geq -7$ and wrote an equivalent inequality in terms of $x$. We also selected the values that make the inequality true and provided the correct answer. By following these steps, you can solve any inequality and find the values that make it true.

Frequently Asked Questions

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 $ax + b \geq c$ or $ax + b \leq c$, where $a$, $b$, and $c$ are constants. A quadratic inequality is an inequality that can be written in the form $ax^2 + bx + c \geq 0$ or $ax^2 + bx + c \leq 0$, where $a$, $b$, and $c$ are constants.

Q: How do I solve a quadratic inequality?

A: To solve a quadratic inequality, you can use the following steps:

1. Factor the quadratic expression, if possible.
2. Set each factor equal to zero and solve for $x$.
3. Use a number line or a graph to determine the intervals where the inequality is true.
4. Write the solution in interval notation.

Q: What is the difference between a rational inequality and a radical inequality?

A: A rational inequality is an inequality that can be written in the form $\frac{ax + b}{cx + d} \geq 0$ or $\frac{ax + b}{cx + d} \leq 0$, where $a$, $b$, $c$, and $d$ are constants. A radical inequality is an inequality that can be written in the form $\sqrt{ax + b} \geq c$ or $\sqrt{ax + b} \leq c$, where $a$, $b$, and $c$ are constants.

Q: How do I solve a rational inequality?

A: To solve a rational inequality, you can use the following steps:

1. Factor the numerator and denominator, if possible.
2. Set each factor equal to zero and solve for $x$.
3. Use a number line or a graph to determine the intervals where the inequality is true.
4. Write the solution in interval notation.

Q: How do I solve a radical inequality?

A: To solve a radical inequality, you can use the following steps:

1. Isolate the radical expression.
2. Square both sides of the inequality, if possible.
3. Solve the resulting inequality.
4. Check the solution by substituting it back into the original inequality.

Additional Resources

• Khan Academy: Inequalities
• Mathway: Inequalities
• Wolfram Alpha: Inequalities

References

• Larson, R., & Hostetler, R. P. (2015). College algebra. Cengage Learning.
• Sullivan, M. (2016). College algebra and trigonometry. Pearson Education.
• Anton, H., & Rorres, C. (2016). Elementary linear algebra. Wiley.
  Solving Inequalities: A Q&A Guide =====================================

Introduction

In our previous article, we discussed how to solve the inequality $-x \geq -7$ and wrote an equivalent inequality in terms of $x$. We also selected the values that make the inequality true and provided the correct answer. In this article, we will continue to provide more information and answer frequently asked questions about solving inequalities.

Q&A

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 $ax + b \geq c$ or $ax + b \leq c$, where $a$, $b$, and $c$ are constants. A quadratic inequality is an inequality that can be written in the form $ax^2 + bx + c \geq 0$ or $ax^2 + bx + c \leq 0$, where $a$, $b$, and $c$ are constants.

Q: How do I solve a quadratic inequality?

A: To solve a quadratic inequality, you can use the following steps:

1. Factor the quadratic expression, if possible.
2. Set each factor equal to zero and solve for $x$.
3. Use a number line or a graph to determine the intervals where the inequality is true.
4. Write the solution in interval notation.

Q: What is the difference between a rational inequality and a radical inequality?

A: A rational inequality is an inequality that can be written in the form $\frac{ax + b}{cx + d} \geq 0$ or $\frac{ax + b}{cx + d} \leq 0$, where $a$, $b$, $c$, and $d$ are constants. A radical inequality is an inequality that can be written in the form $\sqrt{ax + b} \geq c$ or $\sqrt{ax + b} \leq c$, where $a$, $b$, and $c$ are constants.

Q: How do I solve a rational inequality?

A: To solve a rational inequality, you can use the following steps:

1. Factor the numerator and denominator, if possible.
2. Set each factor equal to zero and solve for $x$.
3. Use a number line or a graph to determine the intervals where the inequality is true.
4. Write the solution in interval notation.

Q: How do I solve a radical inequality?

A: To solve a radical inequality, you can use the following steps:

1. Isolate the radical expression.
2. Square both sides of the inequality, if possible.
3. Solve the resulting inequality.
4. Check the solution by substituting it back into the original inequality.

Q: What is the difference between a linear inequality and a system of linear inequalities?

A: A linear inequality is an inequality that can be written in the form $ax + b \geq c$ or $ax + b \leq c$, where $a$, $b$, and $c$ are constants. A system of linear inequalities is a set of two or more linear inequalities that must be satisfied simultaneously.

Q: How do I solve a system of linear inequalities?

A: To solve a system of linear inequalities, you can use the following steps:

1. Graph each inequality on a number line or a coordinate plane.
2. Find the intersection of the two graphs.
3. Write the solution in interval notation.

Q: What is the difference between a quadratic inequality and a system of quadratic inequalities?

A: A quadratic inequality is an inequality that can be written in the form $ax^2 + bx + c \geq 0$ or $ax^2 + bx + c \leq 0$, where $a$, $b$, and $c$ are constants. A system of quadratic inequalities is a set of two or more quadratic inequalities that must be satisfied simultaneously.

Q: How do I solve a system of quadratic inequalities?

A: To solve a system of quadratic inequalities, you can use the following steps:

1. Factor the quadratic expressions, if possible.
2. Set each factor equal to zero and solve for $x$.
3. Use a number line or a graph to determine the intervals where the inequality is true.
4. Write the solution in interval notation.

Additional Resources

• Khan Academy: Inequalities
• Mathway: Inequalities
• Wolfram Alpha: Inequalities

References

• Larson, R., & Hostetler, R. P. (2015). College algebra. Cengage Learning.
• Sullivan, M. (2016). College algebra and trigonometry. Pearson Education.
• Anton, H., & Rorres, C. (2016). Elementary linear algebra. Wiley.

Conclusion

Solving inequalities is an important topic in mathematics that can be used to model real-world problems. In this article, we provided more information and answered frequently asked questions about solving inequalities. We also discussed the differences between linear inequalities, quadratic inequalities, rational inequalities, and radical inequalities. By following the steps outlined in this article, you can solve any inequality and find the values that make it true.