Solve $x + 17 \geq 22$, And Then Graph The Solutions.What Are The Solutions? Select:A. $x \ \textless \ $ $\square$ B. $x \leq$ $\square$

Introduction

In mathematics, inequalities are a fundamental concept that deals with the comparison of two or more mathematical expressions. In this article, we will focus on solving linear inequalities, specifically the inequality $x + 17 \geq 22$. We will also graph the solutions to visualize the inequality.

What are Linear Inequalities?

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, and $x$ is the variable. Linear inequalities can be solved using various methods, including algebraic manipulation and graphical representation.

Solving the Inequality $x + 17 \geq 22$

To solve the inequality $x + 17 \geq 22$, we need to isolate the variable $x$ on one side of the inequality. We can do this by subtracting 17 from both sides of the inequality.

x + 17 - 17 ≥ 22 - 17
x ≥ 5

Therefore, the solution to the inequality $x + 17 \geq 22$ is $x \geq 5$.

Graphing the Solutions

To graph the solutions, we need to plot the line $x = 5$ on a number line. The line $x = 5$ is a vertical line that passes through the point (5, 0).

  |---------------|
  |       5       |
  |---------------|

The solutions to the inequality $x \geq 5$ are all the points to the right of the line $x = 5$. This can be represented as:

  |---------------|
  |       5       |
  |---------------|
  |  x ≥ 5       |
  |---------------|

Conclusion

In this article, we solved the linear inequality $x + 17 \geq 22$ and graphed the solutions. We found that the solution to the inequality is $x \geq 5$. We also visualized the solutions by plotting the line $x = 5$ on a number line.

What are the Solutions?

The solutions to the inequality $x + 17 \geq 22$ are:

• $x \geq 5$

Select the Correct Answer

Based on the solution to the inequality, the correct answer is:

• B. $x \leq$ $\boxed{5}$
  Solving Inequalities: A Q&A Guide =====================================

Introduction

In our previous article, we solved the linear inequality $x + 17 \geq 22$ and graphed the solutions. In this article, we will provide a Q&A guide to help you understand the concept of solving inequalities and graphing the solutions.

Q: What is a linear 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, and $x$ is the variable.

Q: How do I solve a linear inequality?

A: To solve a linear inequality, you need to isolate the variable $x$ on one side of the inequality. You can do this by adding or subtracting the same value to both sides of the inequality.

Q: What is the difference between $x \geq 5$ and $x > 5$?

A: The inequality $x \geq 5$ means that $x$ is greater than or equal to 5, while the inequality $x > 5$ means that $x$ is strictly greater than 5.

Q: How do I graph the solutions to a linear inequality?

A: To graph the solutions to a linear inequality, you need to plot the line that represents the boundary of the inequality. If the inequality is of the form $x \geq c$ or $x \leq c$, you need to plot a vertical line at $x = c$. If the inequality is of the form $y \geq c$ or $y \leq c$, you need to plot a horizontal line at $y = c$.

Q: What is the significance of the boundary line in graphing the solutions?

A: The boundary line represents the point at which the inequality changes from true to false or vice versa. It is an important concept in graphing the solutions to linear inequalities.

Q: Can I have multiple boundary lines in graphing the solutions?

A: Yes, you can have multiple boundary lines in graphing the solutions. For example, if you have the inequality $x \geq 2$ and $x \leq 5$, you need to plot two vertical lines at $x = 2$ and $x = 5$.

Q: How do I determine the direction of the inequality when graphing the solutions?

A: To determine the direction of the inequality when graphing the solutions, you need to test a point on either side of the boundary line. If the point satisfies the inequality, then the region on that side of the boundary line is the solution region.

Q: Can I have a negative coefficient in a linear inequality?

A: Yes, you can have a negative coefficient in a linear inequality. For example, the inequality $-x \geq 5$ is a linear inequality with a negative coefficient.

Q: How do I solve a linear inequality with a negative coefficient?

A: To solve a linear inequality with a negative coefficient, you need to multiply both sides of the inequality by -1. This will change the direction of the inequality.

Conclusion

In this article, we provided a Q&A guide to help you understand the concept of solving inequalities and graphing the solutions. We covered various topics, including the definition of linear inequalities, solving linear inequalities, graphing the solutions, and more. We hope that this guide has been helpful in clarifying any doubts you may have had about solving inequalities and graphing the solutions.

Frequently Asked Questions

• What is a linear inequality?
• How do I solve a linear inequality?
• What is the difference between $x \geq 5$ and $x > 5$?
• How do I graph the solutions to a linear inequality?
• What is the significance of the boundary line in graphing the solutions?
• Can I have multiple boundary lines in graphing the solutions?
• How do I determine the direction of the inequality when graphing the solutions?
• Can I have a negative coefficient in a linear inequality?
• How do I solve a linear inequality with a negative coefficient?

Answers

• 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, and $x$ is the variable.
• To solve a linear inequality, you need to isolate the variable $x$ on one side of the inequality.
• The inequality $x \geq 5$ means that $x$ is greater than or equal to 5, while the inequality $x > 5$ means that $x$ is strictly greater than 5.
• To graph the solutions to a linear inequality, you need to plot the line that represents the boundary of the inequality.
• The boundary line represents the point at which the inequality changes from true to false or vice versa.
• Yes, you can have multiple boundary lines in graphing the solutions.
• To determine the direction of the inequality when graphing the solutions, you need to test a point on either side of the boundary line.
• Yes, you can have a negative coefficient in a linear inequality.
• To solve a linear inequality with a negative coefficient, you need to multiply both sides of the inequality by -1.