Which Graph Shows The Solution To The Inequality { -3x - 7 \ \textless \ 20$}$?

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Introduction to Inequalities

Inequalities are mathematical expressions that compare two values using greater than, less than, greater than or equal to, or less than or equal to symbols. They are used to describe relationships between variables and can be solved using various methods, including algebraic manipulation and graphical representation. In this article, we will focus on solving the inequality $-3x - 7 < 20$ and determining which graph shows the solution.

Understanding the Inequality

The given inequality is $-3x - 7 < 20$. To solve this inequality, we need to isolate the variable $x$ on one side of the inequality sign. We can do this by adding $7$ to both sides of the inequality, which gives us $-3x < 27$. Next, we divide both sides of the inequality by $-3$, which gives us $x > -9$. Note that when we divide or multiply an inequality by a negative number, we need to reverse the direction of the inequality sign.

Graphing the Inequality

To graph the inequality $x > -9$, we need to draw a number line and mark the point $-9$ with an open circle. This is because the inequality is greater than, and we are looking for all values of $x$ that are greater than $-9$. We then draw an arrow to the right of the point $-9$ to indicate that all values of $x$ greater than $-9$ are part of the solution.

Types of Graphs

There are two main types of graphs that can be used to represent the solution to an inequality: a number line graph and a coordinate plane graph. A number line graph is a simple graph that consists of a number line with points marked at regular intervals. A coordinate plane graph, on the other hand, is a graph that consists of a grid of horizontal and vertical lines that intersect at right angles.

Number Line Graph

A number line graph is a simple and effective way to represent the solution to an inequality. To create a number line graph, we need to draw a number line and mark the point $-9$ with an open circle. We then draw an arrow to the right of the point $-9$ to indicate that all values of $x$ greater than $-9$ are part of the solution.

Coordinate Plane Graph

A coordinate plane graph is a more complex graph that consists of a grid of horizontal and vertical lines that intersect at right angles. To create a coordinate plane graph, we need to draw a grid of horizontal and vertical lines and mark the point $-9$ with an open circle. We then draw an arrow to the right of the point $-9$ to indicate that all values of $x$ greater than $-9$ are part of the solution.

Which Graph Shows the Solution?

Based on the above discussion, we can conclude that the graph that shows the solution to the inequality $-3x - 7 < 20$ is a number line graph with an open circle at the point $-9$ and an arrow to the right of the point $-9$. This graph represents all values of $x$ that are greater than $-9$.

Conclusion

In conclusion, solving an inequality involves isolating the variable on one side of the inequality sign and then graphing the solution using a number line graph or a coordinate plane graph. In this article, we focused on solving the inequality $-3x - 7 < 20$ and determining which graph shows the solution. We found that the graph that shows the solution is a number line graph with an open circle at the point $-9$ and an arrow to the right of the point $-9$.

Frequently Asked Questions

• Q: What is the solution to the inequality $-3x - 7 < 20$? A: The solution to the inequality $-3x - 7 < 20$ is $x > -9$.
• Q: Which graph shows the solution to the inequality $-3x - 7 < 20$? A: The graph that shows the solution to the inequality $-3x - 7 < 20$ is a number line graph with an open circle at the point $-9$ and an arrow to the right of the point $-9$.

Final Thoughts

In this article, we discussed how to solve the inequality $-3x - 7 < 20$ and determine which graph shows the solution. We found that the graph that shows the solution is a number line graph with an open circle at the point $-9$ and an arrow to the right of the point $-9$. We hope that this article has provided you with a better understanding of how to solve inequalities and graph their solutions.

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 symbols. They are used to describe relationships between variables and can be solved using various methods, including algebraic manipulation and graphical representation. In this article, we will answer some frequently asked questions about inequalities.

Q&A

Q: What is an inequality?

A: An inequality is a mathematical expression that compares two values using greater than, less than, greater than or equal to, or less than or equal to symbols.

Q: How do I solve an inequality?

A: To solve an inequality, you need to isolate the variable on one side of the inequality sign. You can do this by adding or subtracting the same value to both sides of the inequality, or by multiplying or dividing both sides of the inequality by the same non-zero value.

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

Q: How do I graph an inequality?

A: To graph an inequality, you need to draw a number line or a coordinate plane and mark the point that corresponds to the inequality. You then draw an arrow to the right or left of the point to indicate the direction of the inequality.

Q: What is the solution to an inequality?

A: The solution to an inequality is the set of all values of the variable that satisfy the inequality.

Q: How do I determine the solution to an inequality?

A: To determine the solution to an inequality, you need to isolate the variable on one side of the inequality sign and then graph the inequality.

Q: What is the difference between a strict inequality and a non-strict inequality?

A: A strict inequality is an inequality that is written with a strict inequality symbol, such as {{content}}lt; $ or {{content}}gt; $. A non-strict inequality is an inequality that is written with a non-strict inequality symbol, such as $\leq$ or $\geq$.

Q: How do I solve a system of inequalities?

A: To solve a system of inequalities, you need to solve each inequality separately and then find the intersection of the solutions.

Q: What is the intersection of two sets?

A: The intersection of two sets is the set of all elements that are common to both sets.

Q: How do I find the intersection of two sets?

A: To find the intersection of two sets, you need to identify the elements that are common to both sets and then list them.

Q: What is the union of two sets?

A: The union of two sets is the set of all elements that are in either set.

Q: How do I find the union of two sets?

A: To find the union of two sets, you need to list all the elements that are in either set.

Q: What is the difference between a set and a subset?

A: A set is a collection of unique elements. A subset is a set that is contained within another set.

Q: How do I determine if a set is a subset of another set?

A: To determine if a set is a subset of another set, you need to check if all the elements of the first set are also elements of the second set.

Q: What is the Cartesian product of two sets?

A: The Cartesian product of two sets is the set of all ordered pairs that can be formed by combining one element from each set.

Q: How do I find the Cartesian product of two sets?

A: To find the Cartesian product of two sets, you need to list all the possible ordered pairs that can be formed by combining one element from each set.

Conclusion

In conclusion, inequalities are mathematical expressions that compare two values using greater than, less than, greater than or equal to, or less than or equal to symbols. They are used to describe relationships between variables and can be solved using various methods, including algebraic manipulation and graphical representation. In this article, we answered some frequently asked questions about inequalities and provided examples to illustrate the concepts.

Final Thoughts

In this article, we discussed some frequently asked questions about inequalities and provided examples to illustrate the concepts. We hope that this article has provided you with a better understanding of inequalities and how to solve them. If you have any further questions, please don't hesitate to ask.